# ERGM terms cross-reference

#### statnet.org

#### 07/28/2014

This document is an automatically generated cross reference for the ergm model terms from the stanet project. The source for this data and additional descriptions are in the `?ergm.terms` help file or the ergm manual.

## Interactive searching

It is possible to search the `ergm-terms` help page and search for specific categories of terms using the `search.ergmTerms` command. For example to find all the terms that mention ‘triangle’ in their description:

    search.ergmTerms(keyword='triangle')

    ## Found  9  matching ergm terms:
    ## ctriple(attr=NULL, diff=FALSE, levels=NULL)
    ##  Cyclic triples
    ##
    ## ctriad()
    ##  Cyclic triples
    ##
    ## localtriangle(x)
    ##  Triangles within neighborhoods
    ##
    ## opentriad()
    ##  Open triads
    ##
    ## threetrail(keep=NULL, levels=NULL)
    ##  Three-trails
    ##
    ## triangle(attr=NULL, diff=FALSE, levels=NULL)
    ##  Triangles
    ##
    ## tripercent(attr=NULL, diff=FALSE, levels=NULL)
    ##  Triangle percentage
    ##
    ## ttriple(attr=NULL, diff=FALSE, levels=NULL)
    ##  Transitive triples
    ##
    ## ttriad()
    ##  Transitive triples

Or to find all of the dyad-independent bipartite terms:

    search.ergmTerms(categories=c('bipartite','dyad-independent'))

    ## Found  15  matching ergm terms:
    ## b1cov(attr)
    ##  Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
    ##
    ## b1cov(attr, form="sum")
    ##  Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
    ##
    ## b1factor(attr, base=1, levels=-1)
    ##  Factor attribute effect for the first mode in a bipartite (aka two-mode) network
    ##
    ## b1factor(attr, base=1, levels=-1, form="sum")
    ##  Factor attribute effect for the first mode in a bipartite (aka two-mode) network
    ##
    ## b1nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1,)
    ##  Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
    ##
    ## b1sociality(nodes=-1)
    ##  Degree
    ##
    ## b1sociality(nodes=-1, form="sum")
    ##  Degree
    ##
    ## b2cov(attr)
    ##  Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
    ##
    ## b2cov(attr, form="sum")
    ##  Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
    ##
    ## b2factor(attr, base=1, levels=-1)
    ##  Factor attribute effect for the second mode in a bipartite (aka two-mode) network
    ##
    ## b2factor(attr, base=1, levels=-1, form="sum")
    ##  Factor attribute effect for the second mode in a bipartite (aka two-mode) network
    ##
    ## b2nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1,)
    ##  Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
    ##
    ## b2sociality(nodes=-1)
    ##  Degree
    ##
    ## b2sociality(nodes=-1, form="sum")
    ##  Degree
    ##
    ## diff(attr, pow=1, dir="t-h", sign.action="identity", form ="sum")
    ##  Difference

## Basic / Frequently-used term category matrix

For convenience, this table lists a subset of the most commonly-used ergm terms and categories.

Term name | binary | valued | directed | undirected | bipartite | dyad-independent
--- | --- | --- | --- | --- | --- | ---
absdiff | ✔ |  | ✔ | ✔ |  | ✔
b1cov | ✔ |  |  | ✔ | ✔ | ✔
b1cov |  | ✔ |  | ✔ | ✔ | ✔
b1degree | ✔ |  |  | ✔ | ✔ |
b1factor | ✔ |  |  | ✔ | ✔ | ✔
b1factor |  | ✔ |  | ✔ | ✔ | ✔
b1nodematch | ✔ |  |  | ✔ | ✔ | ✔
b2concurrent | ✔ |  |  | ✔ | ✔ |
b2cov | ✔ |  |  | ✔ | ✔ | ✔
b2cov |  | ✔ |  | ✔ | ✔ | ✔
b2degree | ✔ |  |  | ✔ | ✔ |
b2factor | ✔ |  |  | ✔ | ✔ | ✔
b2factor |  | ✔ |  | ✔ | ✔ | ✔
b2nodematch | ✔ |  |  | ✔ | ✔ | ✔
degree | ✔ |  |  | ✔ |  |
diff | ✔ |  | ✔ | ✔ |  | ✔
edgecov | ✔ |  | ✔ | ✔ |  | ✔
edges | ✔ | ✔ | ✔ | ✔ |  | ✔
gwdegree | ✔ |  |  | ✔ |  |
gwesp | ✔ |  | ✔ | ✔ |  |
idegree | ✔ |  | ✔ |  |  |
isolates | ✔ |  | ✔ | ✔ |  |
mm | ✔ |  | ✔ | ✔ |  | ✔
mm |  | ✔ | ✔ | ✔ |  | ✔
mutual | ✔ |  | ✔ |  |  |
nodecov | ✔ |  | ✔ | ✔ |  | ✔
nodefactor | ✔ |  | ✔ | ✔ |  | ✔
nodeicov | ✔ |  | ✔ |  |  |
nodeifactor | ✔ |  | ✔ |  |  | ✔
nodematch | ✔ |  | ✔ | ✔ |  | ✔
nodemix | ✔ |  | ✔ | ✔ |  | ✔
odegree | ✔ |  | ✔ |  |  |
triangle | ✔ |  | ✔ | ✔ |  |

## Complete term category matrix

This table lists the complete set of terms available in the ergm package. In HTML versions, clicking on a term name will jump to its definition.

Term name | binary | dyad-independent | frequently-used | directed | undirected | quantitative nodal attribute | valued | categorical nodal attribute | curved | triad-related | bipartite | quantitative nodalattribute | deprecated | non-negative
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
absdiff | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |
absdiff |  | ✔ |  | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |
absdiffcat | ✔ | ✔ |  | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
absdiffcat |  | ✔ |  | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |
altkstar | ✔ |  |  |  | ✔ |  |  | ✔ | ✔ |  |  |  |  |
asymmetric | ✔ | ✔ |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
atleast |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
atmost |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
b1concurrent | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1cov | ✔ | ✔ | ✔ |  | ✔ |  |  |  |  |  | ✔ | ✔ |  |
b1cov |  | ✔ | ✔ |  | ✔ | ✔ | ✔ |  |  |  | ✔ |  |  |
b1degrange | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b1degree | ✔ |  | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1dsp | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b1factor | ✔ | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1factor |  | ✔ | ✔ |  | ✔ |  | ✔ | ✔ |  |  | ✔ |  |  |
b1mindegree | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b1nodematch | ✔ | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1sociality | ✔ | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b1sociality |  | ✔ |  |  | ✔ |  | ✔ |  |  |  | ✔ |  |  |
b1star | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1starmix | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b1twostar | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2concurrent | ✔ |  | ✔ |  | ✔ |  |  |  |  |  | ✔ |  |  |
b2cov | ✔ | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  | ✔ |  |  |
b2cov |  | ✔ | ✔ |  | ✔ | ✔ | ✔ |  |  |  | ✔ |  |  |
b2degrange | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b2degree | ✔ |  | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2dsp | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b2factor | ✔ | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2factor |  | ✔ | ✔ |  | ✔ |  | ✔ | ✔ |  |  | ✔ |  |  |
b2mindegree | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b2nodematch | ✔ | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2sociality | ✔ | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
b2sociality |  | ✔ |  |  | ✔ |  | ✔ |  |  |  | ✔ |  |  |
b2star | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2starmix | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
b2twostar | ✔ |  |  |  | ✔ |  |  | ✔ |  |  | ✔ |  |  |
balance | ✔ |  |  | ✔ | ✔ |  |  |  |  | ✔ |  |  |  |
coincidence | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
concurrent | ✔ |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |
concurrentties | ✔ |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |
ctriple | ✔ |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |  |
ctriad | ✔ |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |  |
cycle | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
cyclicalties | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
cyclicalties |  |  |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
cyclicalweights |  |  |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
ddsp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
degrange | ✔ |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |
degree | ✔ |  | ✔ |  | ✔ |  |  | ✔ |  |  |  |  |  |
degree1.5 | ✔ |  |  |  | ✔ |  |  |  |  |  |  |  |  |
degreepopularity | ✔ |  |  |  | ✔ |  |  |  |  |  |  |  | ✔ |
degcrossprod | ✔ |  |  |  | ✔ |  |  |  |  |  |  |  |  |
degcor | ✔ |  |  |  | ✔ |  |  |  |  |  |  |  |  |
density | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
diff | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |
diff |  | ✔ |  | ✔ | ✔ | ✔ | ✔ |  |  |  | ✔ |  |  |
desp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
dgwdsp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
dgwesp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
dgwnsp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
dnsp | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
dsp | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
dyadcov | ✔ | ✔ |  | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
edgecov | ✔ | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |  |
edgecov |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
edges | ✔ | ✔ | ✔ | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
nonzero |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
esp | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
equalto |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
greaterthan |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
gwb1degree | ✔ |  |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |
gwb1dsp | ✔ |  |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |
gwb2degree | ✔ |  |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |
gwb2dsp | ✔ |  |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |
gwdegree | ✔ |  | ✔ |  | ✔ |  |  |  | ✔ |  |  |  |  |
gwdsp | ✔ |  |  | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |
gwesp | ✔ |  | ✔ | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |
gwidegree | ✔ |  |  | ✔ |  |  |  |  | ✔ |  |  |  |  |
gwnsp | ✔ |  |  | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |
gwodegree | ✔ |  |  | ✔ |  |  |  |  | ✔ |  |  |  |  |
hamming | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
hammingmix | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |  |  |  |
idegrange | ✔ |  |  | ✔ |  |  |  | ✔ |  |  |  |  |  |
idegree | ✔ |  | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |  |
idegree1.5 | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
idegreepopularity | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  | ✔ |
ininterval |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
intransitive | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
isolatededges | ✔ |  |  |  | ✔ |  |  |  |  |  | ✔ |  |  |
isolates | ✔ |  | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |  |
istar | ✔ |  |  | ✔ |  |  |  | ✔ |  |  |  |  |  |
kstar | ✔ |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |
smallerthan |  | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
localtriangle | ✔ |  |  | ✔ | ✔ |  |  |  |  | ✔ |  |  |  |
m2star | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
meandeg | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
mm | ✔ | ✔ | ✔ | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
mm |  | ✔ | ✔ | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |
mutual | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |  |  |  |
mutual |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |  |
nearsimmelian | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
nodecov | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |
nodecov |  | ✔ |  | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |
nodemain | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
nodecovar |  |  |  | ✔ | ✔ | ✔ | ✔ |  |  |  |  |  |  |
nodefactor | ✔ | ✔ | ✔ | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
nodefactor |  | ✔ |  | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |
nodeicov | ✔ |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |  |
nodeicov |  |  |  | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |
nodeicovar |  |  |  | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |
nodeifactor | ✔ | ✔ | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |  |
nodeifactor |  | ✔ |  | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |
nodeisqrtcovar |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |  | ✔
nodematch | ✔ | ✔ | ✔ | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
nodematch |  | ✔ |  | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |
match | ✔ | ✔ |  | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
nodemix | ✔ | ✔ | ✔ | ✔ | ✔ |  |  | ✔ |  |  |  |  |  |
nodemix |  | ✔ |  | ✔ | ✔ |  | ✔ | ✔ |  |  |  |  |  |
nodeocov | ✔ | ✔ |  | ✔ |  | ✔ |  |  |  |  |  |  |  |
nodeocov |  | ✔ |  | ✔ |  |  | ✔ |  |  |  |  |  |  |
nodeocovar |  |  |  | ✔ |  | ✔ | ✔ |  |  |  |  |  |  |
nodeofactor | ✔ | ✔ |  | ✔ |  |  |  | ✔ |  |  |  |  |  |
nodeofactor |  | ✔ |  | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |
nodeosqrtcovar |  |  |  | ✔ |  |  | ✔ |  |  |  |  |  |  | ✔
nodesqrtcovar |  |  |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  | ✔
nsp | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
odegrange | ✔ |  |  | ✔ |  |  |  | ✔ |  |  |  |  |  |
odegree | ✔ |  | ✔ | ✔ |  |  |  | ✔ |  |  |  |  |  |
odegree1.5 | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  |  |
odegreepopularity | ✔ |  |  | ✔ |  |  |  |  |  |  |  |  | ✔ |
opentriad | ✔ |  |  |  | ✔ |  |  |  |  | ✔ |  |  |  |
ostar | ✔ |  |  | ✔ |  |  |  | ✔ |  |  |  |  |  |
receiver | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |  |  |  |
receiver |  | ✔ |  | ✔ |  |  | ✔ |  |  |  |  |  |  |
sender | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |  |  |  |
sender |  | ✔ |  | ✔ |  |  | ✔ |  |  |  |  |  |  |
simmelian | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
simmelianties | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
smalldiff | ✔ | ✔ |  | ✔ | ✔ | ✔ |  |  |  |  |  |  |  |
sociality | ✔ | ✔ |  |  | ✔ |  |  | ✔ |  |  |  |  |  |
sociality |  | ✔ |  |  | ✔ |  | ✔ | ✔ |  |  |  |  |  |
sum |  |  |  | ✔ | ✔ |  | ✔ |  |  |  |  |  |  |
threetrail | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |
transitive | ✔ |  |  | ✔ |  |  |  |  |  | ✔ |  |  |  |
transitiveties | ✔ |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |  |
transitiveties |  |  |  | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  |  |
transitiveweights |  |  |  | ✔ | ✔ |  | ✔ |  |  | ✔ |  |  |  | ✔
triadcensus | ✔ |  |  | ✔ | ✔ |  |  |  |  | ✔ |  |  |  |
triangle | ✔ |  | ✔ | ✔ | ✔ |  |  | ✔ |  | ✔ |  |  |  |
tripercent | ✔ |  |  |  | ✔ |  |  | ✔ |  | ✔ |  |  |  |
ttriple | ✔ |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |  |
ttriad | ✔ |  |  | ✔ |  |  |  | ✔ |  | ✔ |  |  |  |
twopath | ✔ |  |  | ✔ | ✔ |  |  |  |  |  |  |  |  |

## Term definitions table

This table lists full definitions for all of the terms along with their tags. Note that some terms may have multiple versions (e.g. valued vs. binary) with slightly different arguments and will be listed more than once with the same definition.

Description | Categories
--- | ---

absdiff(attr, pow=1)

Absolute difference: The `attr` argument specifies a quantitative attribute (see Specifying Vertex Attributes and Levels for details). This term adds one network statistic to the model equaling the sum of `abs(attr[i]-attr[j])^pow` for all edges (i,j) in the network.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, dyad-independent, frequently-used, directed, undirected, quantitative nodal attribute

absdiff(attr, pow=1, form =“sum”)

Absolute difference: The `attr` argument specifies a quantitative attribute (see Specifying Vertex Attributes and Levels for details). This term adds one network statistic to the model equaling the sum of `abs(attr[i]-attr[j])^pow` for all edges (i,j) in the network.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, dyad-independent, directed, undirected, quantitative nodal attribute

absdiffcat(attr, base=NULL, levels=NULL)

Categorical absolute difference: The `attr` argument specifies a quantitative attribute (see Specifying Vertex Attributes and Levels for details). This term adds one statistic for every possible nonzero distinct value of `abs(attr[i]-attr[j])` in the network; the value of each such statistic is the number of edges in the network with the corresponding absolute difference. The optional argument `levels` specifies which nonzero differences to include in or exclude from the model (see Specifying Vertex Attributes and Levels for details). For example, if the possible values of `abs(attr[i]-attr[j])` are 0, 0.5, 3, 3.5, and 10, then to omit 0.5 and 10 one could set `levels=2:3` (we wish to retain the second and third nonzero difference, when differences are sorted in increasing order). Note that this term should generally be used only when the quantitative attribute has a limited number of possible values; an example is the `“Grade”` attribute of the `faux.mesa.high` or `faux.magnolia.high` datasets.

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

binary, dyad-independent, directed, undirected, categorical nodal attribute

absdiffcat(attr, base=NULL, levels=NULL, form=“sum”)

Categorical absolute difference: The `attr` argument specifies a quantitative attribute (see Specifying Vertex Attributes and Levels for details). This term adds one statistic for every possible nonzero distinct value of `abs(attr[i]-attr[j])` in the network; the value of each such statistic is the number of edges in the network with the corresponding absolute difference. The optional argument `levels` specifies which nonzero differences to include in or exclude from the model (see Specifying Vertex Attributes and Levels for details). For example, if the possible values of `abs(attr[i]-attr[j])` are 0, 0.5, 3, 3.5, and 10, then to omit 0.5 and 10 one could set `levels=2:3` (we wish to retain the second and third nonzero difference, when differences are sorted in increasing order). Note that this term should generally be used only when the quantitative attribute has a limited number of possible values; an example is the `“Grade”` attribute of the `faux.mesa.high` or `faux.magnolia.high` datasets.

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

valued, dyad-independent, directed, undirected, categorical nodal attribute

altkstar(lambda, fixed=FALSE)

Alternating k-star: This term adds one network statistic to the model equal to a weighted alternating sequence of k-star statistics with weight parameter `lambda`. This is the version given in Snijders et al. (2006). The `gwdegree` and `altkstar` produce mathematically equivalent models, as long as they are used together with the `edges` (or `kstar(1)`) term, yet the interpretation of the `gwdegree` parameters is slightly more straightforward than the interpretation of the `altkstar` parameters. For this reason, we recommend the use of the `gwdegree` instead of `altkstar`. See Section 3 and especially equation (13) of Hunter (2007) for details. The optional argument `fixed` indicates whether the `decay` parameter is fixed at the given value, or is to be fit as a curved exponential family model (see Hunter and Handcock, 2006). The default is `FALSE`, which means the scale parameter is not fixed and thus the model is a CEF model. This term can only be used with undirected networks.

binary, undirected, curved, categorical nodal attribute

asymmetric(attr=NULL, diff=FALSE, keep=NULL, levels=NULL)

Asymmetric dyads: This term adds one network statistic to the model equal to the number of pairs of actors for which exactly one of (i,j) or (j,i) exists. This term can only be used with directed networks. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified, only asymmetric pairs that match on the vertex attribute `attr` are counted. The optional modifiers `diff` and `levels` are used in the same way as for the `nodematch` term; refer to this term for details and an example.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

binary, directed, dyad-independent, triad-related

atleast(threshold=0) Number of dyads with values greater than or equal to a threshold Adds one statistic equaling to the number of dyads whose values equal or exceed `threshold`. | valued, directed, undirected, dyad-independent
atmost(threshold=0) Number of dyads with values less than or equal to a threshold Adds one statistic equaling to the number of dyads whose values equal or are exceeded by `threshold`. | valued, directed, undirected, dyad-independent

b1concurrent(by=NULL, levels=NULL)

Concurrent node count for the first mode in a bipartite (aka two-mode) network: This term adds one network statistic to the model, equal to the number of nodes in the first mode of the network with degree 2 or higher. The first mode of a bipartite network object is sometimes known as the “actor” mode. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details); it functions just like the `by` argument of the `b1degree` term. Without the optional argument, this statistic is equivalent to `b1mindegree(2)`. This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, categorical nodal attribute

b1cov(attr)

Main effect of a covariate for the first mode in a bipartite (aka two-mode) network: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(i)` for all edges (i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see `b1factor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, undirected, bipartite, dyad-independent, quantitative nodalattribute, frequently-used

b1cov(attr, form=“sum”)

Main effect of a covariate for the first mode in a bipartite (aka two-mode) network: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(i)` for all edges (i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see `b1factor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, undirected, bipartite, dyad-independent, quantitative nodal attribute, frequently-used

b1degrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Degree range for the first mode in a bipartite (a.k.a. two-mode) network: The `from` and `to` arguments are vectors of distinct integers (or `+Inf`, for `to` (its default)). If one of the vectors has length 1, it is recycled to the length of the other. Otherwise, they must have the same length. This term adds one network statistic to the model for each element of `from` (or `to`); the ith such statistic equals the number of nodes of the first mode (“actors”) in the network of degree greater than or equal to `from[i]` but strictly less than `to[i]`, i.e. with edge count in semiopen interval `[from,to)`. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute.

This term can only be used with bipartite networks; for directed networks see `idegrange` and `odegrange`. For undirected networks, see `degrange`, and see `b2degrange` for degrees of the second mode (“events”).

binary, bipartite, undirected

b1degree(d, by=NULL, levels=NULL)

Degree for the first mode in a bipartite (aka two-mode) network: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes of degree `d[i]` in the first mode of a bipartite network, i.e. with exactly `d[i]` edges. The first mode of a bipartite network object is sometimes known as the “actor” mode. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then each node’s degree is tabulated only with other nodes having the same value of the `by` attribute.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, categorical nodal attribute, frequently-used

b1dsp(d)

Dyadwise shared partners for dyads in the first bipartition: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of dyads in the first bipartition with exactly `d[i]` shared partners. (Those shared partners, of course, must be members of the second bipartition.) This term can only be used with bipartite networks.

binary, bipartite, undirected

b1factor(attr, base=1, levels=-1)

Factor attribute effect for the first mode in a bipartite (aka two-mode) network: The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. Each of these statistics gives the number of times a node with that attribute in the first mode of the network appears in an edge. The first mode of a bipartite network object is sometimes known as the “actor” mode.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `b1factor(“fruit”, levels=-(2:3))`, `b1factor(“fruit”, levels=c(1,4))`, and `b1factor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, dyad-independent, frequently-used, categorical nodal attribute

b1factor(attr, base=1, levels=-1, form=“sum”)

Factor attribute effect for the first mode in a bipartite (aka two-mode) network: The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. Each of these statistics gives the number of times a node with that attribute in the first mode of the network appears in an edge. The first mode of a bipartite network object is sometimes known as the “actor” mode.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `b1factor(“fruit”, levels=-(2:3))`, `b1factor(“fruit”, levels=c(1,4))`, and `b1factor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with undirected bipartite networks.

valued, bipartite, undirected, dyad-independent, frequently-used, categorical nodal attribute

b1mindegree(d)

Minimum degree for the first mode in a bipartite (aka two-mode) network: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes in the first mode of a bipartite network with at least degree `d[i]`. The first mode of a bipartite network object is sometimes known as the “actor” mode.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected

b1nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1,)

Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network: This term is introduced in Bomiriya et al (2014). The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). Out of the two arguments (discount parameters) `alpha` and `beta`, both of which take values from [0,1], only one should be set at a time. If none is set to a value other than 1, this term will simply be a homophily based two-star statistic. This term adds one statistic to the model unless `diff` is set to `TRUE`, in which case the term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. To include only the attribute values you wish, use the `levels` arguments.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

If an `alpha` discount parameter is used, each of these statistics gives the sum of the number of common second-mode nodes raised to the power `alpha` for each pair of first-mode nodes with that attribute. If a `beta` discount parameter is used, each of these statistics gives half the sum of the number of two-paths with two first-mode nodes with that attribute as the two ends of the two path raised to the power `beta` for each edge in the network. The `byb2attr` argument specifies a second mode categorical attribute. Setting this argument will separate the orginal statistics based on the values of the set second mode attribute— i.e. for example, if `diff` is `FALSE`, then the sum of all the statistics for each level of this second-mode attribute will be equal to the original `b1nodematch` statistic where `byb2attr` set to `NULL`. This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, dyad-independent, categorical nodal attribute, frequently-used

b1sociality(nodes=-1)

Degree: This term adds one network statistic for each node in the first bipartition, equal to the number of ties of that node. By default, `nodes=-1` means that the statistic for the first node will be omitted, but this argument may be changed to control which statistics are included. The `nodes` argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels for details), where both the attribute and the sorted unique values are the vector of vertex indices `1:nb1`, where `nb1` is the size of the first bipartition. This term can only be used with bipartite networks. For directed networks, see `sender` and `receiver`. For unipartite networks, see `sociality`.

binary, bipartite, undirected, dyad-independent

b1sociality(nodes=-1, form=“sum”)

Degree: This term adds one network statistic for each node in the first bipartition, equal to the number of ties of that node. By default, `nodes=-1` means that the statistic for the first node will be omitted, but this argument may be changed to control which statistics are included. The `nodes` argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels for details), where both the attribute and the sorted unique values are the vector of vertex indices `1:nb1`, where `nb1` is the size of the first bipartition. This term can only be used with bipartite networks. For directed networks, see `sender` and `receiver`. For unipartite networks, see `sociality`.

valued, bipartite, undirected, dyad-independent

b1star(k, attr=NULL, levels=NULL)

k-Stars for the first mode in a bipartite (aka two-mode) network: The `k` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `k`. The ith such statistic counts the number of distinct `k[i]`-stars whose center node is in the first mode of the network. The first mode of a bipartite network object is sometimes known as the “actor” mode. A k-star is defined to be a center node N and a set of k different nodes {O[1], …, O[k]} such that the ties {N, O[i]} exist for i=1, …, k. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then the count is over the number of k-stars (with center node in the first mode) where all nodes have the same value of the attribute. This term can only be used for undirected bipartite networks. Note that `b1star(1)` is equal to `b2star(1)` and to `edges`.

binary, bipartite, undirected, categorical nodal attribute

b1starmix(k, attr, base=NULL, diff=TRUE)

Mixing matrix for k-stars centered on the first mode of a bipartite network: Only a single value of k is allowed. This term counts all k-stars in which the b2 nodes (called events in some contexts) are homophilous in the sense that they all share the same value of `attr`. However, the b1 node (in some contexts, the actor) at the center of the k-star does NOT have to have the same value as the b2 nodes; indeed, the values taken by the b1 nodes may be completely distinct from those of the b2 nodes, which allows for the use of this term in cases where there are two separate nodal attributes, one for the b1 nodes and another for the b2 nodes (in this case, however, these two attributes should be combined to form a single nodal attribute, `attr`). A different statistic is created for each value of `attr` seen in a b1 node, even if no k-stars are observed with this value. Whether a different statistic is created for each value seen in a b2 node depends on the value of the `diff` argument: When `diff=TRUE`, the default, a different statistic is created for each value and thus the behavior of this term is reminiscent of the `nodemix` term, from which it takes its name; when `diff=FALSE`, all homophilous k-stars are counted together, though these k-stars are still categorized according to the value of the central b1 node.

binary, bipartite, undirected, categorical nodal attribute

b1twostar(b1attr, b2attr, base=NULL, b1levels=NULL, b2levels=NULL, levels2=NULL)

Two-star census for central nodes centered on the first mode of a bipartite network: This term takes two nodal attributes (see Specifying Vertex Attributes and Levels for details), one for b1 nodes (actors in some contexts) and one for b2 nodes (events in some contexts). Only `b1attr` is required; if `b2attr` is not passed, it is assumed to be the same as `b1attr`. Assuming that there are n_1 values of `b1attr` among the b1 nodes and n_2 values of `b2attr` among the b2 nodes, then the total number of distinct categories of two stars according to these two attributes is n_1(n_2)(n_2+1)/2. By default, this model term creates a distinct statistic counting each of these categories. The `b1levels`, `b2levels`, `base`, and `levels2` arguments may be used to leave some of these categories out (see Specifying Vertex Attributes and Levels for details).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`. The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels2` are passed, `levels2` overrides `base`.

binary, bipartite, undirected, categorical nodal attribute

b2concurrent(by=NULL)

Concurrent node count for the second mode in a bipartite (aka two-mode) network: This term adds one network statistic to the model, equal to the number of nodes in the second mode of the network with degree 2 or higher. The second mode of a bipartite network object is sometimes known as the “event” mode. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details); it functions just like the `by` argument of the `b2degree` term. Without the optional argument, this statistic is equivalent to `b2mindegree(2)`.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, frequently-used

b2cov(attr)

Main effect of a covariate for the second mode in a bipartite (aka two-mode) network: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(j)` for all edges (i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see `b2factor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, undirected, bipartite, dyad-independent, quantitative nodal attribute, frequently-used

b2cov(attr, form=“sum”)

Main effect of a covariate for the second mode in a bipartite (aka two-mode) network: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(j)` for all edges (i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see `b2factor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, undirected, bipartite, dyad-independent, quantitative nodal attribute, frequently-used

b2degrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Degree range for the second mode in a bipartite (a.k.a. two-mode) network: The `from` and `to` arguments are vectors of distinct integers (or `+Inf`, for `to` (its default)). If one of the vectors has length 1, it is recycled to the length of the other. Otherwise, they must have the same length. This term adds one network statistic to the model for each element of `from` (or `to`); the ith such statistic equals the number of nodes of the second mode (“events”) in the network of degree greater than or equal to `from[i]` but strictly less than `to[i]`, i.e. with edge count in semiopen interval `[from,to)`. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute.

This term can only be used with bipartite networks; for directed networks see `idegrange` and `odegrange`. For undirected networks, see `degrange`, and see `b1degrange` for degrees of the first mode (“actors”).

binary, bipartite, undirected

b2degree(d, by=NULL)

Degree for the second mode in a bipartite (aka two-mode) network: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes of degree `d[i]` in the second mode of a bipartite network, i.e. with exactly `d[i]` edges. The second mode of a bipartite network object is sometimes known as the “event” mode. The optional term `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then each node’s degree is tabulated only with other nodes having the same value of the `by` attribute.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, categorical nodal attribute, frequently-used

b2dsp(d)

Dyadwise shared partners for dyads in the second bipartition: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of dyads in the second bipartition with exactly `d[i]` shared partners. (Those shared partners, of course, must be members of the first bipartition.) This term can only be used with bipartite networks.

binary, bipartite, undirected

b2factor(attr, base=1, levels=-1)

Factor attribute effect for the second mode in a bipartite (aka two-mode) network : The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. Each of these statistics gives the number of times a node with that attribute in the second mode of the network appears in an edge. The second mode of a bipartite network object is sometimes known as the “event” mode.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `b2factor(“fruit”, levels=-(2:3))`, `b2factor(“fruit”, levels=c(1,4))`, and `b2factor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, dyad-independent, categorical nodal attribute, frequently-used

b2factor(attr, base=1, levels=-1, form=“sum”)

Factor attribute effect for the second mode in a bipartite (aka two-mode) network : The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. Each of these statistics gives the number of times a node with that attribute in the second mode of the network appears in an edge. The second mode of a bipartite network object is sometimes known as the “event” mode.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `b2factor(“fruit”, levels=-(2:3))`, `b2factor(“fruit”, levels=c(1,4))`, and `b2factor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with undirected bipartite networks.

valued, bipartite, undirected, dyad-independent, categorical nodal attribute, frequently-used

b2mindegree(d)

Minimum degree for the second mode in a bipartite (aka two-mode) network: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes in the second mode of a bipartite network with at least degree `d[i]`. The second mode of a bipartite network object is sometimes known as the “event” mode.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected

b2nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1,)

Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network: This term is introduced in Bomiriya et al (2014). The `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). Out of the two arguments (discount parameters) `alpha` and `beta`, both which takes values from [0,1], only one should be set at a time. If none is set to a value other than 1, this term will simply be a homophily based two-star statistic. This term adds one statistic to the model unless `diff` is set to `TRUE`, in which case the term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute. To include only the attribute values you wish, use the `levels` argument.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

If an `alpha` discount parameter is used, each of these statistics gives the sum of the number of common first-mode nodes raised to the power `alpha` for each pair of second-mode nodes with that attribute. If a `beta` discount parameter is used, each of these statistics gives half the sum of the number of two-paths with two second-mode nodes with that attribute as the two ends of the two path raised to the power `beta` for each edge in the network. The `byb1attr` argument specifies a first mode categorical attribute. Setting this argument will separate the orginal statistics based on the values of the set first mode attribute— i.e. for example, if `diff` is `FALSE`, then the sum of all the statistics for each level of this first-mode attribute will be equal to the original `b2nodematch` statistic where `byb1attr` set to `NULL`.

This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, dyad-independent, categorical nodal attribute, frequently-used

b2sociality(nodes=-1)

Degree: This term adds one network statistic for each node in the second bipartition, equal to the number of ties of that node. By default, `nodes=-1` means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The `nodes` argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels for details), where both the attribute and the sorted unique values are the vector of vertex indices `(nb1 + 1):n`, where `nb1` is the size of the first bipartition and `n` is the total number of nodes in the network. Thus `nodes=120` will include only the statistic for the 120th node in the second biparition, while `nodes=I(120)` will include only the statistic for the 120th node in the entire network. This term can only be used with undirected bipartite networks. For directed networks, see `sender` and `receiver`. For unipartite networks, see `sociality`.

binary, bipartite, undirected, dyad-independent

b2sociality(nodes=-1, form=“sum”)

Degree: This term adds one network statistic for each node in the second bipartition, equal to the number of ties of that node. By default, `nodes=-1` means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The `nodes` argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels for details), where both the attribute and the sorted unique values are the vector of vertex indices `(nb1 + 1):n`, where `nb1` is the size of the first bipartition and `n` is the total number of nodes in the network. Thus `nodes=120` will include only the statistic for the 120th node in the second biparition, while `nodes=I(120)` will include only the statistic for the 120th node in the entire network. This term can only be used with undirected bipartite networks. For directed networks, see `sender` and `receiver`. For unipartite networks, see `sociality`.

valued, bipartite, undirected, dyad-independent

b2star(k, attr=NULL, levels=NULL)

k-Stars for the second mode in a bipartite (aka two-mode) network: The `k` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `k`. The ith such statistic counts the number of distinct `k[i]`-stars whose center node is in the second mode of the network. The second mode of a bipartite network object is sometimes known as the “event” mode. A k-star is defined to be a center node N and a set of k different nodes {O[1], …, O[k]} such that the ties {N, O[i]} exist for i=1, …, k. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then the count is over the number of k-stars (with center node in the second mode) where all nodes have the same value of the attribute. This term can only be used for undirected bipartite networks. Note that `b2star(1)` is equal to `b1star(1)` and to `edges`.

binary, bipartite, undirected, categorical nodal attribute

b2starmix(k, attr, base=NULL, diff=TRUE) Mixing matrix for k-stars centered on the second mode of a bipartite network: This term is exactly the same as `b1starmix` except that the roles of b1 and b2 are reversed. | binary, bipartite, undirected, categorical nodal attribute
b2twostar(b1attr, b2attr, base=NULL, b1levels=NULL, b2levels=NULL, levels2=NULL) Two-star census for central nodes centered on the second mode of a bipartite network: This term is exactly the same as `b1twostar` except that the roles of b1 and b2 are reversed. | binary, bipartite, undirected, categorical nodal attribute

balance()

Balanced triads: This term adds one network statistic to the model equal to the number of triads in the network that are balanced. The balanced triads are those of type `102` or `300` in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see `?triad.classify` in the `{sna}` package. For an undirected network, the balanced triads are those with an odd number of ties (i.e., 1 and 3).

binary, triad-related, directed, undirected

coincidence(levels=NULL,active=0)

Coincident node count for the second mode in a bipartite (aka two-mode) network: By default this term adds one network statistic to the model for each pair of nodes of mode two. It is equal to the number of (first mode) mutual partners of that pair. The first mode of a bipartite network object is sometimes known as the “actor” mode and the seconds as the “event” mode. So this is the number of actors going to both events in the pair. The optional argument `levels` specifies which pairs of nodes in mode two to include (see Specifying Vertex Attributes and Levels for details). The second optional argument, `active`, selects pairs for which the observed count is at least `active`. If both `levels` and `active` are specified, then `active` is ignored. (Thus, indices passed as `levels` should correspond to indices when `levels` = NULL and `active` = 0.) This term can only be used with undirected bipartite networks.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, bipartite, undirected

concurrent(by=NULL, levels=NULL)

Concurrent node count: This term adds one network statistic to the model, equal to the number of nodes in the network with degree 2 or higher. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details); it functions just like the `by` argument of the `degree` term. This term can only be used with undirected networks.

binary, undirected, categorical nodal attribute

concurrentties(by=NULL, levels=NULL)

Concurrent tie count: This term adds one network statistic to the model, equal to the number of ties incident on each actor beyond the first. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details); it functions just like the `by` argument of the `degree` term. This term can only be used with undirected networks.

binary, undirected, categorical nodal attribute

ctriple(attr=NULL, diff=FALSE, levels=NULL)

Cyclic triples: By default, this term adds one statistic to the model, equal to the number of cyclic triples in the network, defined as a set of edges of the form {(i,j), (j,k), (k,i)}. Note that for all directed networks, `triangle` is equal to `ttriple+ctriple`, so at most two of these three terms can be in a model. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, then the statistic is the number of cyclic triples where all three nodes have the same value of the attribute. If `attr` is specified and `diff` is `TRUE`, then one statistic is added to the model for each value of `attr` (or each value of `attr` specified by `levels` if that argument is passed), equal to the number of cyclic triples where all three nodes have that value of the attribute. This term can only be used with directed networks.

binary, directed, triad-related, categorical nodal attribute

ctriad()

Cyclic triples: By default, this term adds one statistic to the model, equal to the number of cyclic triples in the network, defined as a set of edges of the form {(i,j), (j,k), (k,i)}. Note that for all directed networks, `triangle` is equal to `ttriple+ctriple`, so at most two of these three terms can be in a model. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, then the statistic is the number of cyclic triples where all three nodes have the same value of the attribute. If `attr` is specified and `diff` is `TRUE`, then one statistic is added to the model for each value of `attr` (or each value of `attr` specified by `levels` if that argument is passed), equal to the number of cyclic triples where all three nodes have that value of the attribute. This term can only be used with directed networks.

binary, directed, triad-related, categorical nodal attribute

cycle(k, semi=FALSE)

k-Cycle Census: The `k` argument must be a vector of integers giving the cycle lengths to count. Directed cycle lengths may range from `2` to `N` (the network size); undirected cycle lengths and semicycle lengths may range from `3` to `N`; length 2 semicycles are not currently supported. Note that directed 2-cycles are equivalent to mutual dyads.

This term adds one network statistic to the model for each value of `k`, corresponding to the number of `k`-cycles (or, alternately, semicycles) in the graph.

The optional argument `semi` is a logical indicating whether semicycles (rather than directed cycles) should be counted; this is ignored in the undirected case.

This term can be used with either directed or undirected networks.

binary, directed, undirected

cyclicalties(attr=NULL, levels=NULL)

Cyclical ties: This term adds one statistic, equal to the number of ties i–>j such that there exists a two-path from j to i. (Related to the `ttriple` term.) The binary version takes a nodal attribute `attr`, and, if given, all three nodes involved (i, j, and the node on the two-path) must match on this attribute in order for i–>j to be counted. The binary version of this term can only be used with directed networks. The valued version can be used with both directed and undirected.

binary, directed

cyclicalties(threshold=0)

Cyclical ties: This term adds one statistic, equal to the number of ties i–>j such that there exists a two-path from j to i. (Related to the `ttriple` term.) The binary version takes a nodal attribute `attr`, and, if given, all three nodes involved (i, j, and the node on the two-path) must match on this attribute in order for i–>j to be counted. The binary version of this term can only be used with directed networks. The valued version can be used with both directed and undirected.

valued, directed, undirected

cyclicalweights(twopath=“min”,combine=“max”,affect=“min”)

Cyclical weights: This statistic implements the cyclical weights statistic, like that defined by Krivitsky (2012), Equation 13, but with the focus dyad being y_{j,i} rather than y_{i,j}. The currently implemented options for `twopath` is the minimum of the constituent dyads (`“min”`) or their geometric mean (`“geomean”`); for `combine`, the maximum of the 2-path strengths (`“max”`) or their sum (`“sum”`); and for `affect`, the minimum of the focus dyad and the combined strength of the two paths (`“min”`) or their geometric mean (`“geomean”`). For each of these options, the first (and the default) is more stable but also more conservative, while the second is more sensitive but more likely to induce a multimodal distribution of networks.

valued, directed, undirected

ddsp(d, type=“OTP”)

Directed dyadwise shared partners: This term adds one network statistic to the model for each element in `d` where the ith such statistic equals the number of dyads in the network with exactly `d[i]` shared partners. This term can only be used with directed networks.

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

binary, directed

degrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Degree range: The `from` and `to` arguments are vectors of distinct integers (or `+Inf`, for `to` (its default)). If one of the vectors has length 1, it is recycled to the length of the other. Otherwise, they must have the same length. This term adds one network statistic to the model for each element of `from` (or `to`); the ith such statistic equals the number of nodes in the network of degree greater than or equal to `from[i]` but strictly less than `to[i]`, i.e. with edges in semiopen interval `[from,to)`. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute.

This term can only be used with undirected networks; for directed networks see `idegrange` and `odegrange`. This term can be used with bipartite networks, and will count nodes of both first and second mode in the specified degree range. To count only nodes of the first mode (“actors”), use `b1degrange` and to count only those fo the second mode (“events”), use `b2degrange`.

binary, undirected, categorical nodal attribute

degree(d, by=NULL, homophily=FALSE, levels=NULL)

Degree: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes in the network of degree `d[i]`, i.e. with exactly `d[i]` edges. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with undirected networks; for directed networks see `idegree` and `odegree`.

binary, undirected, categorical nodal attribute, frequently-used

degree1.5() Degree to the 3/2 power: This term adds one network statistic to the model equaling the sum over the actors of each actor’s degree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is an undirected analog to the terms of Snijders et al. (2010), equations (11) and (12). This term can only be used with undirected networks. | binary, undirected
degreepopularity() Degree popularity (deprecated): see `degree1.5`. | binary, undirected, deprecated
degcrossprod() Degree Cross-Product: This term adds one network statistic equal to the mean of the cross-products of the degrees of all pairs of nodes in the network which are tied. Only coded for undirected networks. | binary, undirected
degcor() Degree Correlation: This term adds one network statistic equal to the correlation of the degrees of all pairs of nodes in the network which are tied. Only coded for undirected networks. | binary, undirected
density() Density: This term adds one network statistic equal to the density of the network. For undirected networks, `density` equals `kstar(1)` or `edges` divided by n(n-1)/2; for directed networks, `density` equals `edges` or `istar(1)` or `ostar(1)` divided by n(n-1). | binary, dyad-independent, directed, undirected

diff(attr, pow=1, dir=“t-h”, sign.action=“identity”)

Difference: The `attr` argument specifies a quantitative vertex attribute (see Specifying Vertex Attributes and Levels for details). For values of `pow` other than `0`, this term adds one network statistic to the model, equaling the sum, over directed edges (i,j), of `sign.action(attr[i]-attr[j])^pow` if `dir` is `“t-h”` (the default), `“tail-head”`, or `“b1-b2”` and of `sign.action(attr[j]-attr[i])^pow` if `“h-t”`, `“head-tail”`, or `“b2-b1”`. That is, the argument `dir` determines which vertex’s attribute is subtracted from which, with tail being the origin of a directed edge and head being its destination, and bipartite networks’ edges being treated as going from the first part (b1) to the second (b2).

If `pow==0`, the exponentiation is replaced by the signum function: `+1` if the difference is positive, `0` if there is no difference, and `-1` if the difference is negative. Note that this function is applied after the `sign.action`. The comparison is exact, so when using calculated values of `attr`, ensure that values that you want to be considered equal are, in fact, equal.

The following `sign.actions` are possible:

`“identity”` (the default)

  no transformation of the difference regardless of sign

`“abs”`

  absolute value of the difference: equivalent to the `absdiff` term

`“posonly”`

  positive differences are kept, negative differences are replaced by 0

`“negonly”`

  negative differences are kept, positive differences are replaced by 0

Note that this term may not be meaningful for unipartite undirected networks unless `sign.action==“abs”`. When used on such a network, it behaves as if all edges were directed, going from the lower-indexed vertex to the higher-indexed vertex.

binary, dyad-independent, frequently-used, directed, undirected, quantitative nodal attribute

diff(attr, pow=1, dir=“t-h”, sign.action=“identity”, form =“sum”)

Difference: The `attr` argument specifies a quantitative vertex attribute (see Specifying Vertex Attributes and Levels for details). For values of `pow` other than `0`, this term adds one network statistic to the model, equaling the sum, over directed edges (i,j), of `sign.action(attr[i]-attr[j])^pow` if `dir` is `“t-h”` (the default), `“tail-head”`, or `“b1-b2”` and of `sign.action(attr[j]-attr[i])^pow` if `“h-t”`, `“head-tail”`, or `“b2-b1”`. That is, the argument `dir` determines which vertex’s attribute is subtracted from which, with tail being the origin of a directed edge and head being its destination, and bipartite networks’ edges being treated as going from the first part (b1) to the second (b2).

If `pow==0`, the exponentiation is replaced by the signum function: `+1` if the difference is positive, `0` if there is no difference, and `-1` if the difference is negative. Note that this function is applied after the `sign.action`. The comparison is exact, so when using calculated values of `attr`, ensure that values that you want to be considered equal are, in fact, equal.

The following `sign.actions` are possible:

`“identity”` (the default)

  no transformation of the difference regardless of sign

`“abs”`

  absolute value of the difference: equivalent to the `absdiff` term

`“posonly”`

  positive differences are kept, negative differences are replaced by 0

`“negonly”`

  negative differences are kept, positive differences are replaced by 0

Note that this term may not be meaningful for unipartite undirected networks unless `sign.action==“abs”`. When used on such a network, it behaves as if all edges were directed, going from the lower-indexed vertex to the higher-indexed vertex.

valued, dyad-independent, directed, undirected, bipartite, quantitative nodal attribute

desp(d, type=“OTP”)

Directed edgewise shared partners: This term adds one network statistic to the model for each element in `d` where the ith such statistic equals the number of edges in the network with exactly `d[i]` shared partners. This term can only be used with directed networks.

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

binary, directed

dgwdsp(decay=0, fixed=FALSE, cutoff=30, type=“OTP”)

Geometrically weighted dyadwise shared partner distribution: This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution with decay parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). Note that the GWDSP statistic is equal to the sum of GWNSP plus GWESP.

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

The optional argument `cutoff` sets the number of underlying DSP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, directed

dgwesp(decay=0, fixed=FALSE, cutoff=30, type=“OTP”)

Geometrically weighted edgewise shared partner distribution: This term adds a statistic equal to the geometrically weighted edgewise (not dyadwise) shared partner distribution with decay parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006).

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

The optional argument `cutoff` sets the number of underlying ESP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, directed

dgwnsp(decay=0, fixed=FALSE, cutoff=30, type=“OTP”)

Geometrically weighted non-edgewise shared partner distribution: This term is just like gwesp and gwdsp except it adds a statistic equal to the geometrically weighted nonedgewise (that is, over dyads that do not have an edge) shared partner distribution with decay parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006).

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

The optional argument `cutoff` sets the number of underlying NSP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, directed

dnsp(d, type=“OTP”)

Directed non-edgewise shared partners: This term adds one network statistic to the model for each element in `d` where the ith such statistic equals the number of non-edges in the network with exactly `d[i]` shared partners. This term can only be used with directed networks.

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the `type` argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the `relevent` package):

Outgoing Two-path (`“OTP”`)

  vertex k is an OTP shared partner of ordered pair (i,j) iff i->k->j. Also known as “transitive shared partner”.

Incoming Two-path (`“ITP”`)

  vertex k is an ITP shared partner of ordered pair (i,j) iff j->k->i. Also known as “cyclical shared partner”

Reciprocated Two-path (`“RTP”`)

  vertex k is an RTP shared partner of ordered pair (i,j) iff i<->k<->j.

Outgoing Shared Partner (`“OSP”`)

  vertex k is an OSP shared partner of ordered pair (i,j) iff i->k, j->k.

Incoming Shared Partner (`“ISP”`)

  vertex k is an ISP shared partner of ordered pair (i,j) iff k->i, k->j.

By default, outgoing two-paths (`“OTP”`) are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

binary, directed

dsp(d)

Dyadwise shared partners: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of dyads in the network with exactly `d[i]` shared partners. This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) dyad `(i,j)` in a directed graph, the number of shared partners counted by `dsp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `ddsp`.

binary, directed, undirected

dyadcov(x, attrname=NULL)

Dyadic covariate: The `x` argument is either a square matrix of covariates, one for each possible edge in the network, the name of a network attribute of covariates, or a network; if the latter, optional argument `attrname` provides the name of the quantitative edge attribute to use for covariate values (in this case, missing edges in `x` are assigned a covariate value of zero). This term adds three statistics to the model, each equal to the sum of the covariate values for all dyads occupying one of the three possible non-empty dyad states (mutual, upper-triangular asymmetric, and lower-triangular asymmetric dyads, respectively), with the empty or null state serving as a reference category. If the network is undirected, `x` is either a matrix of edgewise covariates, or a network; if the latter, optional argument `attrname` provides the name of the edge attribute to use for edge values. This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network. The `edgecov` and `dyadcov` terms are equivalent for undirected networks.

binary, dyad-independent, directed, undirected, categorical nodal attribute

edgecov(x, attrname=NULL)

Edge covariate: The `x` argument is either a square matrix of covariates, one for each possible edge in the network, the name of a network attribute of covariates, or a network; if the latter, optional argument `attrname` provides the name of the quantitative edge attribute to use for covariate values (in this case, missing edges in `x` are assigned a covariate value of zero). This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network. The `edgecov` term applies to both directed and undirected networks. For undirected networks the covariates are also assumed to be undirected. The `edgecov` and `dyadcov` terms are equivalent for undirected networks.

binary, dyad-independent, directed, undirected, frequently-used

edgecov(x,)

Edge covariate: The `x` argument is either a square matrix of covariates, one for each possible edge in the network, the name of a network attribute of covariates, or a network; if the latter, optional argument `attrname` provides the name of the quantitative edge attribute to use for covariate values (in this case, missing edges in `x` are assigned a covariate value of zero). This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network. The `edgecov` term applies to both directed and undirected networks. For undirected networks the covariates are also assumed to be undirected. The `edgecov` and `dyadcov` terms are equivalent for undirected networks.

valued, directed, undirected, dyad-independent

edges() Edges: This term adds one network statistic equal to the number of edges (i.e. nonzero values) in the network. For undirected networks, `edges` is equal to `kstar(1)`; for directed networks, `edges` is equal to both `ostar(1)` and `istar(1)`. | binary, valued, dyad-independent, directed, undirected, frequently-used
nonzero() Edges: This term adds one network statistic equal to the number of edges (i.e. nonzero values) in the network. For undirected networks, `edges` is equal to `kstar(1)`; for directed networks, `edges` is equal to both `ostar(1)` and `istar(1)`. | valued, directed, undirected, dyad-independent

esp(d)

Edgewise shared partners: This is just like the `dsp` term, except this term adds one network statistic to the model for each element in `d` where the ith such statistic equals the number of edges (rather than dyads) in the network with exactly `d[i]` shared partners. This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) edge `i -> j` in a directed graph, the number of shared partners counted by `esp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `desp`.

binary, directed, undirected

equalto(value=0, tolerance=0) Number of dyads with values equal to a specific value (within tolerance): Adds one statistic equal to the number of dyads whose values are within `tolerance` of `value`, i.e., between `value-tolerance` and `value+tolerance`, inclusive. | valued, directed, undirected, dyad-independent
greaterthan(threshold=0) Number of dyads with values strictly greater than a threshold: Adds one statistic equal to the number of dyads whose values exceed `threshold`. | valued, directed, undirected, dyad-independent

gwb1degree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Geometrically weighted degree distribution for the first mode in a bipartite (aka two-mode) network: This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the `decay` parameter, which should be non-negative, for nodes in the first mode of a bipartite network. The first mode of a bipartite network object is sometimes known as the “actor” mode. The `decay` parameter is the same as theta_s in equation (14) in Hunter (2007). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used as merely the starting value for the estimation in a curved exponential family model (the default).

The optional argument `cutoff` sets the number of underlying degree terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

If `attr` is specified (see Specifying Vertex Attributes and Levels for details) then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, curved

gwb1dsp(decay=0, fixed=FALSE, cutoff=30)

Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition: This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition, with decay parameter `decay` parameter, which should be non-negative. The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can only be used with bipartite networks.

The optional argument `cutoff` sets the number of underlying b1dsp terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, bipartite, undirected, curved

gwb2degree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Geometrically weighted degree distribution for the second mode in a bipartite (aka two-mode) network: This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the which should be non-negative, for nodes in the second mode of a bipartite network. The second mode of a bipartite network object is sometimes known as the “event” mode. The `decay` parameter is the same as theta_s in equation (14) in Hunter (2007). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used as merely the starting value for the estimation in a curved exponential family model (the default).

The optional argument `cutoff` sets the number of underlying degree terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

If `attr` is specified (see Specifying Vertex Attributes and Levels for details) then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with undirected bipartite networks.

binary, bipartite, undirected, curved

gwb2dsp(decay=0, fixed=FALSE, cutoff=30)

Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition: This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition, with decay parameter `decay` parameter, which should be non-negative. The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can only be used with bipartite networks.

The optional argument `cutoff` sets the number of underlying b2dsp terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, bipartite, undirected, curved

gwdegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Geometrically weighted degree distribution: This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the `decay` parameter. The `decay` parameter is the same as theta_s in equation (14) in Hunter (2007). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006).

The optional argument `cutoff` sets the number of underlying degree terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

If `attr` is specified (see Specifying Vertex Attributes and Levels for details) then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with undirected networks.

binary, undirected, curved, frequently-used

gwdsp(decay=0, fixed=FALSE, cutoff=30)

Geometrically weighted dyadwise shared partner distribution: This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution with decay parameter `decay` parameter, which should be non-negative. The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) dyad `(i,j)` in a directed graph, the number of shared partners counted by `gwdsp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `dgwdsp`.

The optional argument `cutoff` sets the number of underlying DSP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, directed, undirected, curved

gwesp(decay=0, fixed=FALSE, cutoff=30)

Geometrically weighted edgewise shared partner distribution: This term is just like `gwdsp` except it adds a statistic equal to the geometrically weighted edgewise (not dyadwise) shared partner distribution with decay parameter `decay` parameter, which should be non-negative. The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) edge `i -> j` in a directed graph, the number of shared partners counted by `gwesp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `dgwesp`.

The optional argument `cutoff` sets the number of underlying ESP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, frequently-used, directed, undirected, curved

gwidegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Geometrically weighted in-degree distribution: This term adds one network statistic to the model equal to the weighted in-degree distribution with decay parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can only be used with directed networks.

The optional argument `cutoff` sets the number of underlying degree terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

If `attr` is specified (see Specifying Vertex Attributes and Levels for details) then separate degree statistics are calculated for nodes having each separate value of the attribute.

binary, directed, curved

gwnsp(decay=0, fixed=FALSE, cutoff=30)

Geometrically weighted nonedgewise shared partner distribution: This term is just like `gwesp` and `gwdsp` except it adds a statistic equal to the geometrically weighted nonedgewise (that is, over dyads that do not have an edge) shared partner distribution with weight parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The optional argument `fixed` indicates whether the `decay` parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is `FALSE`, which means the scale parameter is not fixed and thus the model is a CEF model. This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) non-edge `(i,j)` in a directed graph, the number of shared partners counted by `gwnsp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `dgwnsp`.

The optional argument `cutoff` sets the number of underlying NSP terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

binary, directed, undirected, curved

gwodegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Geometrically weighted out-degree distribution: This term adds one network statistic to the model equal to the weighted out-degree distribution with decay parameter `decay` parameter, which should be non-negative. (this parameter was called `alpha` prior to `ergm 3.7`). The value supplied for this parameter may be fixed (if `fixed=TRUE`), or it may be used instead as the starting value for the estimation of `decay` in a curved exponential family model (when `fixed=FALSE`, the default) (see Hunter and Handcock, 2006). This term can only be used with directed networks.

The optional argument `cutoff` sets the number of underlying degree terms to use in computing the statistics when `fixed=FALSE`, in order to reduce the computational burden. Its default value can also be controlled by the `gw.cutoff` term option control parameter. (See `control.ergm`.)

If `attr` is specified (see Specifying Vertex Attributes and Levels for details) then separate degree statistics are calculated for nodes having each separate value of the attribute.

binary, directed, curved

hamming(x, cov, attrname=NULL)

Hamming distance: This term adds one statistic to the model equal to the weighted or unweighted Hamming distance of the network from the network specified by `x`. (If no argument is given, `x` is taken to be the observed network, i.e., the network on the left side of the ~ in the formula that defines the ERGM.) Unweighted Hamming distance is defined as the total number of pairs (i,j) (ordered or unordered, depending on whether the network is directed or undirected) on which the two networks differ. If the optional argument `cov` is specified, then the weighted Hamming distance is computed instead, where each pair (i,j) contributes a pre-specified weight toward the distance when the two networks differ on that pair. The argument `cov` is either a matrix of edgewise weights or a network; if the latter, the optional argument `attrname` provides the name of the edge attribute to use for weight values.

binary, dyad-independent, directed, undirected

hammingmix(attr, x, base=NULL, levels=NULL, levels2=NULL)

Hamming distance within mixing: By default, this term adds one statistic to the model for every possible pairing of attribute values of the network for the vertex attribute specified by `attr` (see Specifying Vertex Attributes and Levels). Each such statistic is the Hamming distance (i.e., the number of differences) between the appropriate subset of dyads in the network and the corresponding subset in `x`. The ordering of the attribute values is alphabetical by default, but this may be overridden using the `levels` arguments. The optional arguments `levels` and `levels2` allow the user to control what pairings are included (see Specifying Vertex Attributes and Levels), and the order in which they appear. For example `levels2=-2` will omit the second statistic, making it the de facto reference category.

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels2` are passed, `levels2` overrides `base`.

This term can only be used with directed networks.

binary, directed, dyad-independent

idegrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

In-degree range: The `from` and `to` arguments are vectors of distinct integers (or `+Inf`, for `to` (its default)). If one of the vectors has length 1, it is recycled to the length of the other. Otherwise, they must have the same length. This term adds one network statistic to the model for each element of `from` (or `to`); the ith such statistic equals the number of nodes in the network of in-degree greater than or equal to `from[i]` but strictly less than `to[i]`, i.e. with in-edge count in semiopen interval `[from,to)`. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute.

This term can only be used with directed networks; for undirected networks (bipartite and not) see `degrange`. For degrees of specific modes of bipartite networks, see `b1degrange` and `b2degrange`. For in-degrees, see `idegrange`.

binary, directed, categorical nodal attribute

idegree(d, by=NULL, homophily=FALSE, levels=NULL)

In-degree: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes in the network of in-degree `d[i]`, i.e. the number of nodes with exactly `d[i]` in-edges. The optional term `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with directed networks; for undirected networks see `degree`.

binary, directed, categorical nodal attribute, frequently-used

idegree1.5() In-degree to the 3/2 power: This term adds one network statistic to the model equaling the sum over the actors of each actor’s indegree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is analogous to the term of Snijders et al. (2010), equation (12). This term can only be used with directed networks. | binary, directed
idegreepopularity() In-degree popularity (deprecated): see `idegree1.5`. | binary, directed, deprecated

ininterval(lower=-Inf, upper=+Inf, open=)

Number of dyads whose values are in an interval Adds one statistic equaling to the number of dyads whose values are between `lower` and `upper`. Argument `open` is a `logical` vector of length 2 that controls whether the interval is open (exclusive) on the lower and on the upper end, respectively. `open` can also be specified as one of `“[]”`, `“(]”`, `“[)”`, and `“()”`.

valued, directed, undirected, dyad-independent

intransitive()

Intransitive triads: This term adds one statistic to the model, equal to the number of triads in the network that are intransitive. The intransitive triads are those of type `111D`, `201`, `111U`, `021C`, or `030C` in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see `triad.classify` in the `sna` package. Note the distinction from the `ctriple` term. This term can only be used with directed networks.

binary, directed, triad-related

isolatededges() Isolated edges: This term adds one statistic to the model equal to the number of isolated edges in the network, i.e., the number of edges each of whose endpoints has degree 1. This term can only be used with undirected networks. | binary, undirected, bipartite
isolates() Isolates: This term adds one statistic to the model equal to the number of isolates in the network. For an undirected network, an isolate is defined to be any node with degree zero. For a directed network, an isolate is any node with both in-degree and out-degree equal to zero. | binary, directed, undirected, frequently-used

istar(k, attr=NULL, levels=NULL)

In-stars: The `k` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `k`. The ith such statistic counts the number of distinct `k[i]`-instars in the network, where a k-instar is defined to be a node N and a set of k different nodes {O[1], …, O[k]} such that the ties (O_j, N) exist for j=1, …, k. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then the count is over the number of k-instars where all nodes have the same value of the attribute. This term can only be used for directed networks; for undirected networks see `kstar`. Note that `istar(1)` is equal to both `ostar(1)` and `edges`.

binary, directed, categorical nodal attribute

kstar(k, attr=NULL, levels=NULL)

k-Stars: The `k` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `k`. The ith such statistic counts the number of distinct `k[i]`-stars in the network, where a k-star is defined to be a node N and a set of k different nodes {O[1], …, O[k]} such that the ties {N, O_i} exist for i=1, …, k. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then the count is over the number of k-stars where all nodes have the same value of the attribute. This term can only be used for undirected networks; for directed networks, see `istar`, `ostar`, `twopath` and `m2star`. Note that `kstar(1)` is equal to `edges`.

binary, undirected, categorical nodal attribute

smallerthan(threshold=0) Number of dyads with values strictly smaller than a threshold: Adds one statistic equaling to the number of dyads whose values exceeded by `threshold`. | valued, directed, undirected, dyad-independent

localtriangle(x)

Triangles within neighborhoods: This term adds one statistic to the model equal to the number of triangles in the network between nodes “close to” each other. For an undirected network, a local triangle is defined to be any set of three edges between nodal pairs {(i,j), (j,k), (k,i)} that are in the same neighborhood. For a directed network, a triangle is defined as any set of three edges (i,j), (j,k) and either (k{}i) or (k{≤ftarrow}i) where again all nodes are within the same neighborhood. The argument `x` is an undirected network or an symmetric adjacency matrix that specifies whether the two nodes are in the same neighborhood. Note that `triangle`, with or without an argument, is a special case of `localtriangle`.

binary, triad-related, directed, undirected

m2star()

Mixed 2-stars, a.k.a 2-paths: This term adds one statistic to the model, equal to the number of mixed 2-stars in the network, where a mixed 2-star is a pair of distinct edges (i,j), (j,k). A mixed 2-star is sometimes called a 2-path because it is a directed path of length 2 from i to k via j. However, in the case of a 2-path the focus is usually on the endpoints i and k, whereas for a mixed 2-star the focus is usually on the midpoint j. This term can only be used with directed networks; for undirected networks see `kstar(2)`. See also `twopath`.

binary, directed

meandeg() Mean vertex degree: This term adds one network statistic to the model equal to the average degree of a node. Note that this term is a constant multiple of both `edges` and `density`. | binary, dyad-independent, directed, undirected

mm(attrs, levels=NULL, levels2=NULL)

Mixing matrix cells and margins: `attrs` is a two-sided formula whose LHS gives the attribute or attribute function (see Specifying Vertex Attributes and Levels) for the rows of the mixing matrix and whose RHS gives that for its columns. A one-sided formula (e.g., `~A`) is symmetrized (e.g., `A~A`). `levels` similarly specifies the subset of rows and columns to be used. `levels2` can then be used to filter which specific cells of the matrix to include. A two-sided formula with a dot on one side calculates the margins of the mixing matrix, analogously to `nodefactor`, with `A~.` calculating the row/sender/b1 margins and `.~A` calculating the column/receiver/b2 margins.

binary, dyad-independent, frequently-used, directed, undirected, categorical nodal attribute

mm(attrs, levels=NULL, levels2=NULL, form=“sum”)

Mixing matrix cells and margins: `attrs` is a two-sided formula whose LHS gives the attribute or attribute function (see Specifying Vertex Attributes and Levels) for the rows of the mixing matrix and whose RHS gives that for its columns. A one-sided formula (e.g., `~A`) is symmetrized (e.g., `A~A`). `levels` similarly specifies the subset of rows and columns to be used. `levels2` can then be used to filter which specific cells of the matrix to include. A two-sided formula with a dot on one side calculates the margins of the mixing matrix, analogously to `nodefactor`, with `A~.` calculating the row/sender/b1 margins and `.~A` calculating the column/receiver/b2 margins.

valued, dyad-independent, frequently-used, directed, undirected, categorical nodal attribute

mutual(same=NULL, by=NULL, diff=FALSE, keep=NULL, levels=NULL)

Mutuality: In binary ERGMs, equal to the number of pairs of actors i and j for which (i,j) and (j,i) both exist. For valued ERGMs, equal to ∑{i<j} m(y{i,j},y_{j,i}), where m is determined by `form` argument: `“min”` for (y_{i,j},y_{j,i}), `“nabsdiff”` for -|y_{i,j},y_{j,i}|, `“product”` for y_{i,j}y_{j,i}, and `“geometric”` for √{y_{i,j}}√{y_{j,i}}. See Krivitsky (2012) for a discussion of these statistics. `form=“threshold”` simply computes the binary `mutuality` after thresholding at `threshold`.

This term can only be used with directed networks. The binary version also has the following capabilities: if the optional `same` argument is passed (see Specifying Vertex Attributes and Levels for details), only mutual pairs that match on the attribute are counted; separate counts for each unique matching value can be obtained by using `diff=TRUE` with `same`; and if `by` is passed (again, see Specifying Vertex Attributes and Levels), then each node is counted separately for each mutual pair in which it occurs and the counts are tabulated by unique values of the attribute. This means that the sum of the mutual statistics when `by` is used will equal twice the standard mutual statistic. Only one of `same` or `by` may be used, and only the former is affected by `diff`; if both `same` and `by` are passed, `by` is ignored. Finally, if `levels` is passed, this tells which statistics should be kept whenever the `mutual` term would ordinarily result in multiple statistics (see Specifying Vertex Attributes and Levels).

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

binary, directed, frequently-used

mutual(form=“min”,threshold=0)

Mutuality: In binary ERGMs, equal to the number of pairs of actors i and j for which (i,j) and (j,i) both exist. For valued ERGMs, equal to ∑{i<j} m(y{i,j},y_{j,i}), where m is determined by `form` argument: `“min”` for (y_{i,j},y_{j,i}), `“nabsdiff”` for -|y_{i,j},y_{j,i}|, `“product”` for y_{i,j}y_{j,i}, and `“geometric”` for √{y_{i,j}}√{y_{j,i}}. See Krivitsky (2012) for a discussion of these statistics. `form=“threshold”` simply computes the binary `mutuality` after thresholding at `threshold`.

This term can only be used with directed networks. The binary version also has the following capabilities: if the optional `same` argument is passed (see Specifying Vertex Attributes and Levels for details), only mutual pairs that match on the attribute are counted; separate counts for each unique matching value can be obtained by using `diff=TRUE` with `same`; and if `by` is passed (again, see Specifying Vertex Attributes and Levels), then each node is counted separately for each mutual pair in which it occurs and the counts are tabulated by unique values of the attribute. This means that the sum of the mutual statistics when `by` is used will equal twice the standard mutual statistic. Only one of `same` or `by` may be used, and only the former is affected by `diff`; if both `same` and `by` are passed, `by` is ignored. Finally, if `levels` is passed, this tells which statistics should be kept whenever the `mutual` term would ordinarily result in multiple statistics (see Specifying Vertex Attributes and Levels).

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

valued, directed

nearsimmelian() Near simmelian triads: This term adds one statistic to the model equal to the number of near Simmelian triads, as defined by Krackhardt and Handcock (2007). This is a sub-graph of size three which is exactly one tie short of being complete. This term can only be used with directed networks. | binary, directed, triad-related

nodecov(attr)

Main effect of a covariate: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the sum of `attr(i)` and `attr(j)` for all edges (i,j) in the network. For categorical attributes, see `nodefactor`. Note that for directed networks, `nodecov` equals `nodeicov` plus `nodeocov`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, dyad-independent, frequently-used, directed, undirected, quantitative nodal attribute

nodecov(attr, form=“sum”)

Main effect of a covariate: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the sum of `attr(i)` and `attr(j)` for all edges (i,j) in the network. For categorical attributes, see `nodefactor`. Note that for directed networks, `nodecov` equals `nodeicov` plus `nodeocov`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, dyad-independent, directed, undirected, quantitative nodal attribute

nodemain()

Main effect of a covariate: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the sum of `attr(i)` and `attr(j)` for all edges (i,j) in the network. For categorical attributes, see `nodefactor`. Note that for directed networks, `nodecov` equals `nodeicov` plus `nodeocov`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, directed, undirected

nodecovar() Uncentered covariance of dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} (y{i,j}y_{i,k}+y_{k,j}y_{k,j}). This can be viewed as a valued analog of the `kstar(2)` statistic. | valued, directed, undirected, quantitative nodal attribute

nodefactor(attr, base=1, levels=-1)

Factor attribute effect: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears in an edge in the network.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodefactor(“fruit”, levels=-(2:3))`, `nodefactor(“fruit”, levels=c(1,4))`, and `nodefactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

binary, dyad-independent, directed, undirected, categorical nodal attribute, frequently-used

nodefactor(attr, base=1, levels=-1, form=“sum”)

Factor attribute effect: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears in an edge in the network.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodefactor(“fruit”, levels=-(2:3))`, `nodefactor(“fruit”, levels=c(1,4))`, and `nodefactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

dyad-independent, valued, directed, undirected, categorical nodal attribute

nodeicov(attr)

Main effect of a covariate for in-edges: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(j)` for all edges (i,j) in the network. This term may only be used with directed networks. For categorical attributes, see `nodeifactor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, directed, quantitative nodal attribute, frequently-used

nodeicov(attr, form=“sum”)

Main effect of a covariate for in-edges: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(j)` for all edges (i,j) in the network. This term may only be used with directed networks. For categorical attributes, see `nodeifactor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, directed, quantitative nodal attribute

nodeicovar() Uncentered covariance of in-dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} y{k,j}y_{k,j}. This can be viewed as a valued analog of the `istar(2)` statistic. | valued, directed, quantitative nodal attribute

nodeifactor(attr, base=1, levels=-1)

Factor attribute effect for in-edges: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the terminal node of a directed tie.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodeifactor(“fruit”, levels=-(2:3))`, `nodeifactor(“fruit”, levels=c(1,4))`, and `nodeifactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

For an analogous term for quantitative vertex attributes, see `nodeicov`.

binary, dyad-independent, directed, categorical nodal attribute, frequently-used

nodeifactor(attr, base=1, levels=-1, form=“sum”)

Factor attribute effect for in-edges: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the terminal node of a directed tie.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodeifactor(“fruit”, levels=-(2:3))`, `nodeifactor(“fruit”, levels=c(1,4))`, and `nodeifactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

For an analogous term for quantitative vertex attributes, see `nodeicov`.

valued, dyad-independent, directed, categorical nodal attribute

nodeisqrtcovar() Uncentered covariance of square roots of in-dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} √{y{i,j}}√{y_{k,j}}. This can be viewed as a valued analog of the `istar(2)` statistic. | valued, directed, non-negative

nodematch(attr, diff=FALSE, keep=NULL, levels=NULL)

Uniform homophily and differential homophily: The `attr` argument specifies one or more attributes (see Specifying Vertex Attributes and Levels for details). When `diff=FALSE`, this term adds one network statistic to the model, which counts the number of edges (i,j) for which `attr(i)==attr(j)`. This is also called ”uniform homophily,” because each group is assumed to have the same propensity for within-group ties. When multiple attribute names are given, the statistic counts only ties for which all of the attributes match. When `diff=TRUE`, p network statistics are added to the model, where p is the number of unique values of the `attr` attribute. The kth such statistic counts the number of edges (i,j) for which `attr(i) == attr(j) == value(k)`, where `value(k)` is the kth smallest unique value of the `attr` attribute. This is also called ”differential homophily,” because each group is allowed to have a unique propensity for within-group ties. Note that a statistical test of uniform vs. differential homophily should be conducted using the ANOVA function.

By default, matches on all levels k are counted. The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodematch(“fruit”, levels=-(2:3))`, `nodematch(“fruit”, levels=c(1,4))`, and `nodematch(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels. This works for both `diff=TRUE` and `diff=FALSE`.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

binary, dyad-independent, frequently-used, directed, undirected, categorical nodal attribute

nodematch(attr, diff=FALSE, keep=NULL, levels=NULL, form=“sum”)

Uniform homophily and differential homophily: The `attr` argument specifies one or more attributes (see Specifying Vertex Attributes and Levels for details). When `diff=FALSE`, this term adds one network statistic to the model, which counts the number of edges (i,j) for which `attr(i)==attr(j)`. This is also called ”uniform homophily,” because each group is assumed to have the same propensity for within-group ties. When multiple attribute names are given, the statistic counts only ties for which all of the attributes match. When `diff=TRUE`, p network statistics are added to the model, where p is the number of unique values of the `attr` attribute. The kth such statistic counts the number of edges (i,j) for which `attr(i) == attr(j) == value(k)`, where `value(k)` is the kth smallest unique value of the `attr` attribute. This is also called ”differential homophily,” because each group is allowed to have a unique propensity for within-group ties. Note that a statistical test of uniform vs. differential homophily should be conducted using the ANOVA function.

By default, matches on all levels k are counted. The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodematch(“fruit”, levels=-(2:3))`, `nodematch(“fruit”, levels=c(1,4))`, and `nodematch(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels. This works for both `diff=TRUE` and `diff=FALSE`.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

valued, dyad-independent, directed, undirected, categorical nodal attribute

match()

Uniform homophily and differential homophily: The `attr` argument specifies one or more attributes (see Specifying Vertex Attributes and Levels for details). When `diff=FALSE`, this term adds one network statistic to the model, which counts the number of edges (i,j) for which `attr(i)==attr(j)`. This is also called ”uniform homophily,” because each group is assumed to have the same propensity for within-group ties. When multiple attribute names are given, the statistic counts only ties for which all of the attributes match. When `diff=TRUE`, p network statistics are added to the model, where p is the number of unique values of the `attr` attribute. The kth such statistic counts the number of edges (i,j) for which `attr(i) == attr(j) == value(k)`, where `value(k)` is the kth smallest unique value of the `attr` attribute. This is also called ”differential homophily,” because each group is allowed to have a unique propensity for within-group ties. Note that a statistical test of uniform vs. differential homophily should be conducted using the ANOVA function.

By default, matches on all levels k are counted. The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodematch(“fruit”, levels=-(2:3))`, `nodematch(“fruit”, levels=c(1,4))`, and `nodematch(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels. This works for both `diff=TRUE` and `diff=FALSE`.

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`.

binary, directed, dyad-independent, undirected, categorical nodal attribute

nodemix(attr, base=NULL, b1levels=NULL, b2levels=NULL, levels=NULL, levels2=NULL)

Nodal attribute mixing: The `attr` argument specifies one or more categorical vertex attributes (see Specifying Vertex Attributes and Levels for details). By default, this term adds one network statistic to the model for each possible pairing of attribute values. The statistic equals the number of edges in the network in which the nodes have that pairing of values. (When multiple attributes are specified, a statistic is added for each combination of attribute values for those attributes.) In other words, this term produces one statistic for every entry in the mixing matrix for the attribute(s). By default, the ordering of the attribute values is lexicographic: alphabetical (for nominal categories) or numerical (for ordered categories), but this can be overridden using the `levels` arguments. The optional arguments `levels`, `levels2`, `b1levels`, and `b2levels` control what statistics are included in the model, and the order in which they appear. `levels2` apply to all networks; `levels` applies to unipartite networks; `b1levels` and `b2levels` apply to bipartite networks (see Specifying Vertex Attributes and Levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels2` are passed, `levels2` overrides `base`.

binary, dyad-independent, frequently-used, directed, undirected, categorical nodal attribute

nodemix(attr, base=NULL, b1levels=NULL, b2levels=NULL, levels=NULL, levels2=NULL, form=“sum”)

Nodal attribute mixing: The `attr` argument specifies one or more categorical vertex attributes (see Specifying Vertex Attributes and Levels for details). By default, this term adds one network statistic to the model for each possible pairing of attribute values. The statistic equals the number of edges in the network in which the nodes have that pairing of values. (When multiple attributes are specified, a statistic is added for each combination of attribute values for those attributes.) In other words, this term produces one statistic for every entry in the mixing matrix for the attribute(s). By default, the ordering of the attribute values is lexicographic: alphabetical (for nominal categories) or numerical (for ordered categories), but this can be overridden using the `levels` arguments. The optional arguments `levels`, `levels2`, `b1levels`, and `b2levels` control what statistics are included in the model, and the order in which they appear. `levels2` apply to all networks; `levels` applies to unipartite networks; `b1levels` and `b2levels` apply to bipartite networks (see Specifying Vertex Attributes and Levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels2` are passed, `levels2` overrides `base`.

valued, dyad-independent, directed, undirected, categorical nodal attribute

nodeocov(attr)

Main effect of a covariate for out-edges: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(i)` for all edges (i,j) in the network. This term may only be used with directed networks. For categorical attributes, see `nodeofactor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

binary, directed, dyad-independent, quantitative nodal attribute

nodeocov(attr, form=“sum”)

Main effect of a covariate for out-edges: The `attr` argument specifies one or more quantitative attributes (see Specifying Vertex Attributes and Levels for details). This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of `attr(i)` for all edges (i,j) in the network. This term may only be used with directed networks. For categorical attributes, see `nodeofactor`.

Note that `ergm` versions 3.9.4 and earlier used different arguments for this term. See the above section on versioning for invoking the old behavior.

valued, directed, dyad-independent

nodeocovar() Uncentered covariance of out-dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} y{i,j}y_{i,k}. This can be viewed as a valued analog of the `ostar(2)` statistic. | valued, directed, quantitative nodal attribute

nodeofactor(attr, base=1, levels=-1)

Factor attribute effect for out-edges: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the node of origin of a directed tie.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodeofactor(“fruit”, levels=-(2:3))`, `nodeofactor(“fruit”, levels=c(1,4))`, and `nodeofactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with directed networks.

binary, dyad-independent, directed, categorical nodal attribute

nodeofactor(attr, base=1, levels=-1, form=“sum”)

Factor attribute effect for out-edges: The `attr` argument specifies one or more categorical attributes (see Specifying Vertex Attributes and Levels for details). This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the `attr` attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the node of origin of a directed tie.

The optional `levels` argument controls which levels of the attribute should be included and which should be excluded. (See Specifying Vertex Attributes and Levels for details.) For example, if the “fruit” attribute has levels “orange”, “apple”, “banana”, and “pear”, then to include just two levels, one for “apple” and one for “pear”, use any of `nodeofactor(“fruit”, levels=-(2:3))`, `nodeofactor(“fruit”, levels=c(1,4))`, and `nodeofactor(“fruit”, levels=c(“apple”, “pear”))`. Note: if you are using numeric values to specify the levels of a character variable, the levels will correspond to the alphabetically sorted character levels.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including `edges`. The default, `levels=-1`, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either `levels=TRUE` (i.e., keep all levels) or `levels=NULL` (i.e., do not filter levels).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `levels` are passed, `levels` overrides `base`.

This term can only be used with directed networks.

valued, dyad-independent, categorical nodal attribute, directed

nodeosqrtcovar() Uncentered covariance of square roots of out-dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} √{y{i,j}}√{y_{i,k}}. This can be viewed as a valued analog of the `ostar(2)` statistic. | valued, directed, non-negative

nodesqrtcovar(center=TRUE)

Covariance of square roots of dyad values incident on each actor: This term adds one statistic equal to ∑{i,j,k} (√{y{i,j}}√{y_{i,k}}+√{y_{k,j}}√{y_{k,j}}) if `center=FALSE`. This can be viewed as a valued analog of the `kstar(2)` statistic. If `center=TRUE` (the default), the statistic is instead ∑{i,j,k} ((√{y{i,j}}-{√{y}})(√{y_{i,k}}-{√{y}})+(√{y_{k,j}}-{√{y}})(√{y_{k,j}}-{√{y}})), where {√{y}} is the mean of the square root of dyad values.

valued, non-negative, directed, undirected

nsp(d)

Nonedgewise shared partners: This is just like the `dsp` and `esp` terms, except this term adds one network statistic to the model for each element in `d` where the ith such statistic equals the number of non-edges (that is, dyads that do not have an edge) in the network with exactly `d[i]` shared partners. This term can be used with directed and undirected networks.

For directed networks, only outgoing two-path (“OTP”) shared partners are counted. In other words, for a (directed) non-edge `(i,j)` in a directed graph, the number of shared partners counted by `nsp` is the number of nodes `k` that have edges `i -> k -> j`. (These may also be called homogeneous shared partners.) To count other types of shared partners instead, see `dnsp`.

binary, directed, undirected

odegrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Out-degree range: The `from` and `to` arguments are vectors of distinct integers (or `+Inf`, for `to` (its default)). If one of the vectors has length 1, it is recycled to the length of the other. Otherwise, they must have the same length. This term adds one network statistic to the model for each element of `from` (or `to`); the ith such statistic equals the number of nodes in the network of out-degree greater than or equal to `from[i]` but strictly less than `to[i]`, i.e. with out-edge count in semiopen interval `[from,to)`. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute.

This term can only be used with directed networks; for undirected networks (bipartite and not) see `degrange`. For degrees of specific modes of bipartite networks, see `b1degrange` and `b2degrange`. For in-degrees, see `idegrange`.

binary, directed, categorical nodal attribute

odegree(d, by=NULL, homophily=FALSE, levels=NULL)

Out-degree: The `d` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `d`; the ith such statistic equals the number of nodes in the network of out-degree `d[i]`, i.e. the number of nodes with exactly `d[i]` out-edges. The optional argument `by` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified and `homophily` is `TRUE`, then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the `by` attribute. If `by` is specified and `homophily` is `FALSE` (the default), then separate degree statistics are calculated for nodes having each separate value of the attribute. This term can only be used with directed networks; for undirected networks see `degree`.

binary, directed, categorical nodal attribute, frequently-used

odegree1.5() Out-degree to the 3/2 power: This term adds one network statistic to the model equaling the sum over the actors of each actor’s outdegree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is analogous to the term of Snijders et al. (2010), equation (12). This term can only be used with directed networks. | binary, directed
odegreepopularity() Out-degree popularity (deprecated): see `odegree1.5`. | binary, directed, deprecated
opentriad() Open triads: This term adds one statistic to the model equal to the number of 2-stars minus three times the number of triangles in the network. It is currently only implemented for undirected networks. | binary, undirected, triad-related

ostar(k, attr=NULL, levels=NULL)

k-Outstars: The `k` argument is a vector of distinct integers. This term adds one network statistic to the model for each element in `k`. The ith such statistic counts the number of distinct `k[i]`-outstars in the network, where a k-outstar is defined to be a node N and a set of k different nodes {O[1], …, O[k]} such that the ties (N,O_j) exist for j=1, …, k. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If this is specified then the count is the number of k-outstars where all nodes have the same value of the attribute. This term can only be used with directed networks; for undirected networks see `kstar`. Note that `ostar(1)` is equal to both `istar(1)` and `edges`.

binary, directed, categorical nodal attribute

receiver(base=1, nodes=-1)

Receiver effect: This term adds one network statistic for each node equal to the number of in-ties for that node. This measures the popularity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with `edges`, but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the \(p_1\) model (Holland and Leinhardt, 1981). The `base` and `nodes` arguments allow the user to determine which nodes’ statistics should be included or excluded (see Specifying Vertex Attributes and Levels for details). The argument `nodes` is preferred to `base`, although `base` carries a default value of 1 for backwards compatibility. (If both `base` and `nodes` are supplied, then `nodes` overrides `base`.) This term can only be used with directed networks. For undirected networks, see `sociality`.

binary, directed, dyad-independent

receiver(base=1, nodes=-1, form=“sum”)

Receiver effect: This term adds one network statistic for each node equal to the number of in-ties for that node. This measures the popularity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with `edges`, but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the \(p_1\) model (Holland and Leinhardt, 1981). The `base` and `nodes` arguments allow the user to determine which nodes’ statistics should be included or excluded (see Specifying Vertex Attributes and Levels for details). The argument `nodes` is preferred to `base`, although `base` carries a default value of 1 for backwards compatibility. (If both `base` and `nodes` are supplied, then `nodes` overrides `base`.) This term can only be used with directed networks. For undirected networks, see `sociality`.

valued, directed, dyad-independent

sender(base=1, nodes=-1)

Sender effect: This term adds one network statistic for each node equal to the number of out-ties for that node. This measures the activity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with `edges`, but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the \(p_1\) model (Holland and Leinhardt, 1981). The `nodes` arguments allow the user to determine which nodes’ statistics should be included or excluded (see Specifying Vertex Attributes and Levels for details).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `nodes` are passed, `nodes` overrides `base`.

This term can only be used with directed networks. For undirected networks, see `sociality`.

binary, directed, dyad-independent

sender(base=1, nodes=-1, form=“sum”)

Sender effect: This term adds one network statistic for each node equal to the number of out-ties for that node. This measures the activity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with `edges`, but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the \(p_1\) model (Holland and Leinhardt, 1981). The `nodes` arguments allow the user to determine which nodes’ statistics should be included or excluded (see Specifying Vertex Attributes and Levels for details).

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `nodes` are passed, `nodes` overrides `base`.

This term can only be used with directed networks. For undirected networks, see `sociality`.

valued, directed, dyad-independent

simmelian() Simmelian triads: This term adds one statistic to the model equal to the number of Simmelian triads, as defined by Krackhardt and Handcock (2007). This is a complete sub-graph of size three. This term can only be used with directed networks. | binary, directed, triad-related

simmelianties()

Ties in simmelian triads: This term adds one statistic to the model equal to the number of ties in the network that are associated with Simmelian triads, as defined by Krackhardt and Handcock (2007). Each Simmelian has six ties in it but, because Simmelians can overlap in terms of nodes (and associated ties), the total number of ties in these Simmelians is less than six times the number of Simmelians. Hence this is a measure of the clustering of Simmelians (given the number of Simmelians). This term can only be used with directed networks.

binary, triad-related, directed

smalldiff(attr, cutoff)

Number of ties between actors with similar (but not necessarily identical) attribute values: The `attr` argument specifies a quantitative vertex attribute (see Specifying Vertex Attributes and Levels for details). This term adds one statistic, having as its value the number of edges in the network for which the incident actors’ attribute values differ less than `cutoff`; that is, number of edges between `i` to `j` such that `abs(attr[i]-attr[j])<cutoff`.

binary, dyad-independent, directed, undirected, quantitative nodal attribute

sociality(attr=NULL, base=1, levels=NULL, nodes=-1)

Undirected degree: This term adds one network statistic for each node equal to the number of ties of that node. The optional `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). If provided, this term only counts ties between nodes with the same value of the attribute (an actor-specific version of the `nodematch` term), restricted to be one of the values specified by `levels` if `levels` is not `NULL`. This term can only be used with undirected networks. For directed networks, see `sender` and `receiver`. By default, `nodes=-1` means that the statistic for the first node will be omitted, but this argument may be changed to control which statistics are included just as for the `nodes` argument of `sender` and `receiver` terms.

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `nodes` are passed, `nodes` overrides `base`.

binary, undirected, dyad-independent, categorical nodal attribute

sociality(attr=NULL, base=1, levels=NULL, nodes=-1, form=“sum”)

Undirected degree: This term adds one network statistic for each node equal to the number of ties of that node. The optional `attr` argument specifies a categorical vertex attribute (see Specifying Vertex Attributes and Levels for details). If provided, this term only counts ties between nodes with the same value of the attribute (an actor-specific version of the `nodematch` term), restricted to be one of the values specified by `levels` if `levels` is not `NULL`. This term can only be used with undirected networks. For directed networks, see `sender` and `receiver`. By default, `nodes=-1` means that the statistic for the first node will be omitted, but this argument may be changed to control which statistics are included just as for the `nodes` argument of `sender` and `receiver` terms.

The argument `base` is retained for backwards compatibility and may be removed in a future version. When both `base` and `nodes` are passed, `nodes` overrides `base`.

valued, undirected, dyad-independent, categorical nodal attribute

sum(pow=1) Sum of dyad values (optionally taken to a power): This term adds one statistic equal to the sum of dyad values taken to the power `pow`, which defaults to 1. | valued, directed, undirected

threetrail(keep=NULL, levels=NULL)

Three-trails: a.k.a. `threepath`. For an undirected network, this term adds one statistic equal to the number of 3-trails, where a 3-trail is defined as a “trail” of length three that traverses three distinct edges. Note that a 3-trail need not include four distinct nodes; in particular, a triangle counts as three 3-trails. For a directed network, this term adds four statistics (or some subset of these four specified by the `levels` argument), one for each of the four distinct types of directed three-paths. If the nodes of the path are written from left to right such that the middle edge points to the right (R), then the four types are RRR, RRL, LRR, and LRL. That is, an RRR 3-trail is of the form i–>j–>k–>l, and RRL 3-trail is of the form i–>j–>k<–l, etc. Like in the undirected case, there is no requirement that the nodes be distinct in a directed 3-trail. However, the three edges must all be distinct. Thus, a mutual tie i<–>j does not count as a 3-trail of the form i–>j–>i<–j; however, in the subnetwork i<–>j–>k, there are two directed 3-trails, one LRR (k<–j–>i–>j) and one RRR (k<–j–>i–>j).

The argument `keep` is retained for backwards compatibility and may be removed in a future version. When both `keep` and `levels` are passed, `levels` overrides `keep`. This term used to be (inaccurately) called `threepath`. That name has been deprecated and may be removed in a future version.

binary, directed, undirected

transitive()

Transitive triads: This term adds one statistic to the model, equal to the number of triads in the network that are transitive. The transitive triads are those of type `120D`, `030T`, `120U`, or `300` in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see `triad.classify` in the `sna` package. Note the distinction from the `ttriple` term. This term can only be used with directed networks.

binary, directed, triad-related

transitiveties(attr=NULL, levels=NULL)

Transitive ties: This term adds one statistic, equal to the number of ties i–>j such that there exists a two-path from i to j. (Related to the `ttriple` term.) The binary version takes a nodal attribute `attr`, and, if given, all three nodes involved (i, j, and the node on the two-path) must match on this attribute in order for i–>j to be counted. The binary version of this term can only be used with directed networks. The valued version can be used with both directed and undirected.

binary, directed, triad-related, categorical nodal attribute

transitiveties(threshold=0)

Transitive ties: This term adds one statistic, equal to the number of ties i–>j such that there exists a two-path from i to j. (Related to the `ttriple` term.) The binary version takes a nodal attribute `attr`, and, if given, all three nodes involved (i, j, and the node on the two-path) must match on this attribute in order for i–>j to be counted. The binary version of this term can only be used with directed networks. The valued version can be used with both directed and undirected.

valued, directed, undirected, triad-related

transitiveweights(twopath=“min”,combine=“max”,affect=“min”)

Transitive weights: This statistic implements the transitive weights statistic defined by Krivitsky (2012), Equation 13. The currently implemented options for `twopath` is the minimum of the constituent dyads (`“min”`) or their geometric mean (`“geomean”`); for `combine`, the maximum of the 2-path strengths (`“max”`) or their sum (`“sum”`); and for `affect`, the minimum of the focus dyad and the combined strength of the two paths (`“min”`) or their geometric mean (`“geomean”`). For each of these options, the first (and the default) is more stable but also more conservative, while the second is more sensitive but more likely to induce a multimodal distribution of networks.

valued, directed, undirected, non-negative, triad-related

triadcensus(levels)

Triad census: For a directed network, this term adds one network statistic for each of an arbitrary subset of the 16 possible types of triads categorized by Davis and Leinhardt (1972) as `003, 012, 102, 021D, 021U, 021C, 111D, 111U, 030T, 030C, 201, 120D, 120U, 120C, 210,` and `300`. Note that at least one category should be dropped; otherwise a linear dependency will exist among the 16 statistics, since they must sum to the total number of three-node sets. By default, the category `003`, which is the category of completely empty three-node sets, is dropped. This is considered category zero, and the others are numbered 1 through 15 in the order given above. By using the `levels` argument (see Specifying Vertex Attributes and Levels for details), the user may specify a set of terms to add other than the default value of `1:15`. Each statistic is the count of the corresponding triad type in the network. For details on the 16 types, see `?triad.classify` in the `{sna}` package, on which this code is based. For an undirected network, the triad census is over the four types defined by the number of ties (i.e., 0, 1, 2, and 3), and the default is to add `1:3`, which is to say that the 0 is dropped; however, this too may be controlled by changing the `levels` argument.

binary, triad-related, directed, undirected

triangle(attr=NULL, diff=FALSE, levels=NULL)

Triangles: By default, this term adds one statistic to the model equal to the number of triangles in the network. For an undirected network, a triangle is defined to be any set {(i,j), (j,k), (k,i)} of three edges. For a directed network, a triangle is defined as any set of three edges (i,j) and (j,k) and either (k,i) or (i,k). The former case is called a “transitive triple” and the latter is called a “cyclic triple”, so in the case of a directed network, `triangle` equals `ttriple` plus `ctriple` — thus at most two of these three terms can be in a model. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, then the count is restricted to those triples of nodes with equal values of the vertex attribute specified by `attr`. If `attr` is specified and `diff` is `TRUE`, then one statistic is added for each value of `attr` (or each value specified by `levels` if that argument is passed), equal to the number of triangles where all three nodes have that value of the attribute.

binary, frequently-used, triad-related, directed, undirected, categorical nodal attribute

tripercent(attr=NULL, diff=FALSE, levels=NULL)

Triangle percentage: By default, this term adds one statistic to the model equal to 100 times the ratio of the number of triangles in the network to the sum of the number of triangles and the number of 2-stars not in triangles (the latter is considered a potential but incomplete triangle). In case the denominator equals zero, the statistic is defined to be zero. For the definition of triangle, see `triangle`. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, the counts (both numerator and denominator) are restricted to those triples of nodes with equal values of the vertex attribute specified by `attr`. If `attr` is specified and `diff` is `TRUE`, then one statistic is added for each value of `attr` (or each value specified by `levels` if that argument is passed), where the counts (both numerator and denominator) are restricted to those triples of nodes with that value of the vertex attribute specified by `attr`. This is often called the mean correlation coefficient. This term can only be used with undirected networks; for directed networks, it is difficult to define the numerator and denominator in a consistent and meaningful way.

binary, undirected, triad-related, categorical nodal attribute

ttriple(attr=NULL, diff=FALSE, levels=NULL)

Transitive triples: By default, this term adds one statistic to the model, equal to the number of transitive triples in the network, defined as a set of edges {(i,j), (j,k), (i,k)}. Note that `triangle` equals `ttriple+ctriple` for a directed network, so at most two of the three terms can be in a model. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, then the count is over the number of transitive triples where all three nodes have the same value of the attribute. If `attr` is specified and `diff` is `TRUE`, then one statistic is added for each value of `attr` (or each value of `attr` specified by `levels` if that argument is passed), equal to the number of transitive triples where all three nodes have that value of `attr`. This term can only be used with directed networks.

binary, directed, triad-related, categorical nodal attribute

ttriad()

Transitive triples: By default, this term adds one statistic to the model, equal to the number of transitive triples in the network, defined as a set of edges {(i,j), (j,k), (i,k)}. Note that `triangle` equals `ttriple+ctriple` for a directed network, so at most two of the three terms can be in a model. The optional argument `attr` specifies a vertex attribute (see Specifying Vertex Attributes and Levels for details). If `attr` is specified and `diff` is `FALSE`, then the count is over the number of transitive triples where all three nodes have the same value of the attribute. If `attr` is specified and `diff` is `TRUE`, then one statistic is added for each value of `attr` (or each value of `attr` specified by `levels` if that argument is passed), equal to the number of transitive triples where all three nodes have that value of `attr`. This term can only be used with directed networks.

binary, directed, triad-related, categorical nodal attribute

twopath()

2-Paths: This term adds one statistic to the model, equal to the number of 2-paths in the network. For a directed network this is defined as a pair of edges (i,j), (j,k), where i and j must be distinct. That is, it is a directed path of length 2 from i to k via j. For directed networks a 2-path is also a mixed 2-star but the interpretation is usually different; see `m2star`. For undirected networks a twopath is defined as a pair of edges {i,j}, {j,k}. That is, it is an undirected path of length 2 from i to k via j, also known as a 2-star.

binary, directed, undirected

## Term index by category

Note that currently the categories are somewhat ambiguous in their exclusivity. For example, a term marked as ‘directed’ can not be used with an undirected network, but a term not marked with either ‘directed’ or ‘undirected’ can be used with both. (rename to ‘directed-only’ ?)

Jump to category:binary dyad-independent frequently-used directed undirected quantitative nodal attribute valued categorical nodal attribute curved triad-related bipartite quantitative nodalattribute deprecated non-negative

### binary

- absdiff : Absolute difference
- absdiffcat : Categorical absolute difference
- altkstar : Alternating k-star
- asymmetric : Asymmetric dyads
- b1concurrent : Concurrent node count for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1degrange : Degree range for the first mode in a bipartite (a.k.a. two-mode) network
- b1degree : Degree for the first mode in a bipartite (aka two-mode) network
- b1dsp : Dyadwise shared partners for dyads in the first bipartition
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1mindegree : Minimum degree for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b1sociality : Degree
- b1star : k-Stars for the first mode in a bipartite (aka two-mode) network
- b1starmix : Mixing matrix for k-stars centered on the first mode of a bipartite network
- b1twostar : Two-star census for central nodes centered on the first mode of a bipartite network
- b2concurrent : Concurrent node count for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2degrange : Degree range for the second mode in a bipartite (a.k.a. two-mode) network
- b2degree : Degree for the second mode in a bipartite (aka two-mode) network
- b2dsp : Dyadwise shared partners for dyads in the second bipartition
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2mindegree : Minimum degree for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- b2sociality : Degree
- b2star : k-Stars for the second mode in a bipartite (aka two-mode) network
- b2starmix : Mixing matrix for k-stars centered on the second mode of a bipartite network
- b2twostar : Two-star census for central nodes centered on the second mode of a bipartite network
- balance : Balanced triads
- coincidence : Coincident node count for the second mode in a bipartite (aka two-mode) network
- concurrent : Concurrent node count
- concurrentties : Concurrent tie count
- ctriple : Cyclic triples
- ctriad : Cyclic triples
- cycle : k-Cycle Census
- cyclicalties : Cyclical ties
- ddsp :
- degrange : Degree range
- degree : Degree
- degree1.5 : Degree to the 3/2 power
- degreepopularity : Degree popularity (deprecated)
- degcrossprod : Degree Cross-Product
- degcor : Degree Correlation
- density : Density
- diff : Difference
- desp :
- dgwdsp :
- dgwesp :
- dgwnsp :
- dnsp :
- dsp : Dyadwise shared partners
- dyadcov : Dyadic covariate
- edgecov : Edge covariate
- edges : Edges
- esp : Edgewise shared partners
- gwb1degree : Geometrically weighted degree distribution for the first mode in a bipartite (aka two-mode) network
- gwb1dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition
- gwb2degree : Geometrically weighted degree distribution for the second mode in a bipartite (aka two-mode) network
- gwb2dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition
- gwdegree : Geometrically weighted degree distribution
- gwdsp : Geometrically weighted dyadwise shared partner distribution
- gwesp : Geometrically weighted edgewise shared partner distribution
- gwidegree : Geometrically weighted in-degree distribution
- gwnsp : Geometrically weighted nonedgewise shared partner distribution
- gwodegree : Geometrically weighted out-degree distribution
- hamming : Hamming distance
- hammingmix : Hamming distance within mixing
- idegrange : In-degree range
- idegree : In-degree
- idegree1.5 : In-degree to the 3/2 power
- idegreepopularity : In-degree popularity (deprecated)
- intransitive : Intransitive triads
- isolatededges : Isolated edges
- isolates : Isolates
- istar : In-stars
- kstar : k-Stars
- localtriangle : Triangles within neighborhoods
- m2star : Mixed 2-stars, a.k.a 2-paths
- meandeg : Mean vertex degree
- mm : Mixing matrix cells and margins
- mutual : Mutuality
- nearsimmelian : Near simmelian triads
- nodecov : Main effect of a covariate
- nodemain : Main effect of a covariate
- nodefactor : Factor attribute effect
- nodeicov : Main effect of a covariate for in-edges
- nodeifactor : Factor attribute effect for in-edges
- nodematch : Uniform homophily and differential homophily
- match : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodeocov : Main effect of a covariate for out-edges
- nodeofactor : Factor attribute effect for out-edges
- nsp : Nonedgewise shared partners
- odegrange : Out-degree range
- odegree : Out-degree
- odegree1.5 : Out-degree to the 3/2 power
- odegreepopularity : Out-degree popularity (deprecated)
- opentriad : Open triads
- ostar : k-Outstars
- receiver : Receiver effect
- sender : Sender effect
- simmelian : Simmelian triads
- simmelianties : Ties in simmelian triads
- smalldiff : Number of ties between actors with similar (but not necessarily identical) attribute values
- sociality : Undirected degree
- threetrail : Three-trails
- transitive : Transitive triads
- transitiveties : Transitive ties
- triadcensus : Triad census
- triangle : Triangles
- tripercent : Triangle percentage
- ttriple : Transitive triples
- ttriad : Transitive triples
- twopath : 2-Paths

### dyad-independent

- absdiff : Absolute difference
- absdiff : Absolute difference
- absdiffcat : Categorical absolute difference
- absdiffcat : Categorical absolute difference
- asymmetric : Asymmetric dyads
- atleast : Number of dyads with values greater than or equal to a threshol
- atmost : Number of dyads with values less than or equal to a threshol
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b1sociality : Degree
- b1sociality : Degree
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- b2sociality : Degree
- b2sociality : Degree
- density : Density
- diff : Difference
- diff : Difference
- dyadcov : Dyadic covariate
- edgecov : Edge covariate
- edgecov : Edge covariate
- edges : Edges
- nonzero : Edges
- equalto : Number of dyads with values equal to a specific value (within tolerance)
- greaterthan : Number of dyads with values strictly greater than a threshold
- hamming : Hamming distance
- hammingmix : Hamming distance within mixing
- ininterval : Number of dyads whose values are in an interva
- smallerthan : Number of dyads with values strictly smaller than a threshold
- meandeg : Mean vertex degree
- mm : Mixing matrix cells and margins
- mm : Mixing matrix cells and margins
- nodecov : Main effect of a covariate
- nodecov : Main effect of a covariate
- nodefactor : Factor attribute effect
- nodefactor : Factor attribute effect
- nodeifactor : Factor attribute effect for in-edges
- nodeifactor : Factor attribute effect for in-edges
- nodematch : Uniform homophily and differential homophily
- nodematch : Uniform homophily and differential homophily
- match : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodemix : Nodal attribute mixing
- nodeocov : Main effect of a covariate for out-edges
- nodeocov : Main effect of a covariate for out-edges
- nodeofactor : Factor attribute effect for out-edges
- nodeofactor : Factor attribute effect for out-edges
- receiver : Receiver effect
- receiver : Receiver effect
- sender : Sender effect
- sender : Sender effect
- smalldiff : Number of ties between actors with similar (but not necessarily identical) attribute values
- sociality : Undirected degree
- sociality : Undirected degree

### frequently-used

- absdiff : Absolute difference
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1degree : Degree for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b2concurrent : Concurrent node count for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2degree : Degree for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- degree : Degree
- diff : Difference
- edgecov : Edge covariate
- edges : Edges
- gwdegree : Geometrically weighted degree distribution
- gwesp : Geometrically weighted edgewise shared partner distribution
- idegree : In-degree
- isolates : Isolates
- mm : Mixing matrix cells and margins
- mm : Mixing matrix cells and margins
- mutual : Mutuality
- nodecov : Main effect of a covariate
- nodefactor : Factor attribute effect
- nodeicov : Main effect of a covariate for in-edges
- nodeifactor : Factor attribute effect for in-edges
- nodematch : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- odegree : Out-degree
- triangle : Triangles

### directed

- absdiff : Absolute difference
- absdiff : Absolute difference
- absdiffcat : Categorical absolute difference
- absdiffcat : Categorical absolute difference
- asymmetric : Asymmetric dyads
- atleast : Number of dyads with values greater than or equal to a threshol
- atmost : Number of dyads with values less than or equal to a threshol
- balance : Balanced triads
- ctriple : Cyclic triples
- ctriad : Cyclic triples
- cycle : k-Cycle Census
- cyclicalties : Cyclical ties
- cyclicalties : Cyclical ties
- cyclicalweights : Cyclical weights
- ddsp :
- density : Density
- diff : Difference
- diff : Difference
- desp :
- dgwdsp :
- dgwesp :
- dgwnsp :
- dnsp :
- dsp : Dyadwise shared partners
- dyadcov : Dyadic covariate
- edgecov : Edge covariate
- edgecov : Edge covariate
- edges : Edges
- nonzero : Edges
- esp : Edgewise shared partners
- equalto : Number of dyads with values equal to a specific value (within tolerance)
- greaterthan : Number of dyads with values strictly greater than a threshold
- gwdsp : Geometrically weighted dyadwise shared partner distribution
- gwesp : Geometrically weighted edgewise shared partner distribution
- gwidegree : Geometrically weighted in-degree distribution
- gwnsp : Geometrically weighted nonedgewise shared partner distribution
- gwodegree : Geometrically weighted out-degree distribution
- hamming : Hamming distance
- hammingmix : Hamming distance within mixing
- idegrange : In-degree range
- idegree : In-degree
- idegree1.5 : In-degree to the 3/2 power
- idegreepopularity : In-degree popularity (deprecated)
- ininterval : Number of dyads whose values are in an interva
- intransitive : Intransitive triads
- isolates : Isolates
- istar : In-stars
- smallerthan : Number of dyads with values strictly smaller than a threshold
- localtriangle : Triangles within neighborhoods
- m2star : Mixed 2-stars, a.k.a 2-paths
- meandeg : Mean vertex degree
- mm : Mixing matrix cells and margins
- mm : Mixing matrix cells and margins
- mutual : Mutuality
- mutual : Mutuality
- nearsimmelian : Near simmelian triads
- nodecov : Main effect of a covariate
- nodecov : Main effect of a covariate
- nodemain : Main effect of a covariate
- nodecovar : Uncentered covariance of dyad values incident on each actor
- nodefactor : Factor attribute effect
- nodefactor : Factor attribute effect
- nodeicov : Main effect of a covariate for in-edges
- nodeicov : Main effect of a covariate for in-edges
- nodeicovar : Uncentered covariance of in-dyad values incident on each actor
- nodeifactor : Factor attribute effect for in-edges
- nodeifactor : Factor attribute effect for in-edges
- nodeisqrtcovar : Uncentered covariance of square roots of in-dyad values incident on each actor
- nodematch : Uniform homophily and differential homophily
- nodematch : Uniform homophily and differential homophily
- match : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodemix : Nodal attribute mixing
- nodeocov : Main effect of a covariate for out-edges
- nodeocov : Main effect of a covariate for out-edges
- nodeocovar : Uncentered covariance of out-dyad values incident on each actor
- nodeofactor : Factor attribute effect for out-edges
- nodeofactor : Factor attribute effect for out-edges
- nodeosqrtcovar : Uncentered covariance of square roots of out-dyad values incident on each actor
- nodesqrtcovar : Covariance of square roots of dyad values incident on each actor
- nsp : Nonedgewise shared partners
- odegrange : Out-degree range
- odegree : Out-degree
- odegree1.5 : Out-degree to the 3/2 power
- odegreepopularity : Out-degree popularity (deprecated)
- ostar : k-Outstars
- receiver : Receiver effect
- receiver : Receiver effect
- sender : Sender effect
- sender : Sender effect
- simmelian : Simmelian triads
- simmelianties : Ties in simmelian triads
- smalldiff : Number of ties between actors with similar (but not necessarily identical) attribute values
- sum : Sum of dyad values (optionally taken to a power)
- threetrail : Three-trails
- transitive : Transitive triads
- transitiveties : Transitive ties
- transitiveties : Transitive ties
- transitiveweights : Transitive weights
- triadcensus : Triad census
- triangle : Triangles
- ttriple : Transitive triples
- ttriad : Transitive triples
- twopath : 2-Paths

### undirected

- absdiff : Absolute difference
- absdiff : Absolute difference
- absdiffcat : Categorical absolute difference
- absdiffcat : Categorical absolute difference
- altkstar : Alternating k-star
- atleast : Number of dyads with values greater than or equal to a threshol
- atmost : Number of dyads with values less than or equal to a threshol
- b1concurrent : Concurrent node count for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1degrange : Degree range for the first mode in a bipartite (a.k.a. two-mode) network
- b1degree : Degree for the first mode in a bipartite (aka two-mode) network
- b1dsp : Dyadwise shared partners for dyads in the first bipartition
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1mindegree : Minimum degree for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b1sociality : Degree
- b1sociality : Degree
- b1star : k-Stars for the first mode in a bipartite (aka two-mode) network
- b1starmix : Mixing matrix for k-stars centered on the first mode of a bipartite network
- b1twostar : Two-star census for central nodes centered on the first mode of a bipartite network
- b2concurrent : Concurrent node count for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2degrange : Degree range for the second mode in a bipartite (a.k.a. two-mode) network
- b2degree : Degree for the second mode in a bipartite (aka two-mode) network
- b2dsp : Dyadwise shared partners for dyads in the second bipartition
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2mindegree : Minimum degree for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- b2sociality : Degree
- b2sociality : Degree
- b2star : k-Stars for the second mode in a bipartite (aka two-mode) network
- b2starmix : Mixing matrix for k-stars centered on the second mode of a bipartite network
- b2twostar : Two-star census for central nodes centered on the second mode of a bipartite network
- balance : Balanced triads
- coincidence : Coincident node count for the second mode in a bipartite (aka two-mode) network
- concurrent : Concurrent node count
- concurrentties : Concurrent tie count
- cycle : k-Cycle Census
- cyclicalties : Cyclical ties
- cyclicalweights : Cyclical weights
- degrange : Degree range
- degree : Degree
- degree1.5 : Degree to the 3/2 power
- degreepopularity : Degree popularity (deprecated)
- degcrossprod : Degree Cross-Product
- degcor : Degree Correlation
- density : Density
- diff : Difference
- diff : Difference
- dsp : Dyadwise shared partners
- dyadcov : Dyadic covariate
- edgecov : Edge covariate
- edgecov : Edge covariate
- edges : Edges
- nonzero : Edges
- esp : Edgewise shared partners
- equalto : Number of dyads with values equal to a specific value (within tolerance)
- greaterthan : Number of dyads with values strictly greater than a threshold
- gwb1degree : Geometrically weighted degree distribution for the first mode in a bipartite (aka two-mode) network
- gwb1dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition
- gwb2degree : Geometrically weighted degree distribution for the second mode in a bipartite (aka two-mode) network
- gwb2dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition
- gwdegree : Geometrically weighted degree distribution
- gwdsp : Geometrically weighted dyadwise shared partner distribution
- gwesp : Geometrically weighted edgewise shared partner distribution
- gwnsp : Geometrically weighted nonedgewise shared partner distribution
- hamming : Hamming distance
- ininterval : Number of dyads whose values are in an interva
- isolatededges : Isolated edges
- isolates : Isolates
- kstar : k-Stars
- smallerthan : Number of dyads with values strictly smaller than a threshold
- localtriangle : Triangles within neighborhoods
- meandeg : Mean vertex degree
- mm : Mixing matrix cells and margins
- mm : Mixing matrix cells and margins
- nodecov : Main effect of a covariate
- nodecov : Main effect of a covariate
- nodemain : Main effect of a covariate
- nodecovar : Uncentered covariance of dyad values incident on each actor
- nodefactor : Factor attribute effect
- nodefactor : Factor attribute effect
- nodematch : Uniform homophily and differential homophily
- nodematch : Uniform homophily and differential homophily
- match : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodemix : Nodal attribute mixing
- nodesqrtcovar : Covariance of square roots of dyad values incident on each actor
- nsp : Nonedgewise shared partners
- opentriad : Open triads
- smalldiff : Number of ties between actors with similar (but not necessarily identical) attribute values
- sociality : Undirected degree
- sociality : Undirected degree
- sum : Sum of dyad values (optionally taken to a power)
- threetrail : Three-trails
- transitiveties : Transitive ties
- transitiveweights : Transitive weights
- triadcensus : Triad census
- triangle : Triangles
- tripercent : Triangle percentage
- twopath : 2-Paths

### quantitative nodal attribute

- absdiff : Absolute difference
- absdiff : Absolute difference
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- diff : Difference
- diff : Difference
- nodecov : Main effect of a covariate
- nodecov : Main effect of a covariate
- nodecovar : Uncentered covariance of dyad values incident on each actor
- nodeicov : Main effect of a covariate for in-edges
- nodeicov : Main effect of a covariate for in-edges
- nodeicovar : Uncentered covariance of in-dyad values incident on each actor
- nodeocov : Main effect of a covariate for out-edges
- nodeocovar : Uncentered covariance of out-dyad values incident on each actor
- smalldiff : Number of ties between actors with similar (but not necessarily identical) attribute values

### valued

- absdiff : Absolute difference
- absdiffcat : Categorical absolute difference
- atleast : Number of dyads with values greater than or equal to a threshol
- atmost : Number of dyads with values less than or equal to a threshol
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1sociality : Degree
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2sociality : Degree
- cyclicalties : Cyclical ties
- cyclicalweights : Cyclical weights
- diff : Difference
- edgecov : Edge covariate
- edges : Edges
- nonzero : Edges
- equalto : Number of dyads with values equal to a specific value (within tolerance)
- greaterthan : Number of dyads with values strictly greater than a threshold
- ininterval : Number of dyads whose values are in an interva
- smallerthan : Number of dyads with values strictly smaller than a threshold
- mm : Mixing matrix cells and margins
- mutual : Mutuality
- nodecov : Main effect of a covariate
- nodecovar : Uncentered covariance of dyad values incident on each actor
- nodefactor : Factor attribute effect
- nodeicov : Main effect of a covariate for in-edges
- nodeicovar : Uncentered covariance of in-dyad values incident on each actor
- nodeifactor : Factor attribute effect for in-edges
- nodeisqrtcovar : Uncentered covariance of square roots of in-dyad values incident on each actor
- nodematch : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodeocov : Main effect of a covariate for out-edges
- nodeocovar : Uncentered covariance of out-dyad values incident on each actor
- nodeofactor : Factor attribute effect for out-edges
- nodeosqrtcovar : Uncentered covariance of square roots of out-dyad values incident on each actor
- nodesqrtcovar : Covariance of square roots of dyad values incident on each actor
- receiver : Receiver effect
- sender : Sender effect
- sociality : Undirected degree
- sum : Sum of dyad values (optionally taken to a power)
- transitiveties : Transitive ties
- transitiveweights : Transitive weights

### categorical nodal attribute

- absdiffcat : Categorical absolute difference
- absdiffcat : Categorical absolute difference
- altkstar : Alternating k-star
- b1concurrent : Concurrent node count for the first mode in a bipartite (aka two-mode) network
- b1degree : Degree for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b1star : k-Stars for the first mode in a bipartite (aka two-mode) network
- b1starmix : Mixing matrix for k-stars centered on the first mode of a bipartite network
- b1twostar : Two-star census for central nodes centered on the first mode of a bipartite network
- b2degree : Degree for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- b2star : k-Stars for the second mode in a bipartite (aka two-mode) network
- b2starmix : Mixing matrix for k-stars centered on the second mode of a bipartite network
- b2twostar : Two-star census for central nodes centered on the second mode of a bipartite network
- concurrent : Concurrent node count
- concurrentties : Concurrent tie count
- ctriple : Cyclic triples
- ctriad : Cyclic triples
- degrange : Degree range
- degree : Degree
- dyadcov : Dyadic covariate
- idegrange : In-degree range
- idegree : In-degree
- istar : In-stars
- kstar : k-Stars
- mm : Mixing matrix cells and margins
- mm : Mixing matrix cells and margins
- nodefactor : Factor attribute effect
- nodefactor : Factor attribute effect
- nodeifactor : Factor attribute effect for in-edges
- nodeifactor : Factor attribute effect for in-edges
- nodematch : Uniform homophily and differential homophily
- nodematch : Uniform homophily and differential homophily
- match : Uniform homophily and differential homophily
- nodemix : Nodal attribute mixing
- nodemix : Nodal attribute mixing
- nodeofactor : Factor attribute effect for out-edges
- nodeofactor : Factor attribute effect for out-edges
- odegrange : Out-degree range
- odegree : Out-degree
- ostar : k-Outstars
- sociality : Undirected degree
- sociality : Undirected degree
- transitiveties : Transitive ties
- triangle : Triangles
- tripercent : Triangle percentage
- ttriple : Transitive triples
- ttriad : Transitive triples

### curved

- altkstar : Alternating k-star
- gwb1degree : Geometrically weighted degree distribution for the first mode in a bipartite (aka two-mode) network
- gwb1dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition
- gwb2degree : Geometrically weighted degree distribution for the second mode in a bipartite (aka two-mode) network
- gwb2dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition
- gwdegree : Geometrically weighted degree distribution
- gwdsp : Geometrically weighted dyadwise shared partner distribution
- gwesp : Geometrically weighted edgewise shared partner distribution
- gwidegree : Geometrically weighted in-degree distribution
- gwnsp : Geometrically weighted nonedgewise shared partner distribution
- gwodegree : Geometrically weighted out-degree distribution

### triad-related

- asymmetric : Asymmetric dyads
- balance : Balanced triads
- ctriple : Cyclic triples
- ctriad : Cyclic triples
- intransitive : Intransitive triads
- localtriangle : Triangles within neighborhoods
- nearsimmelian : Near simmelian triads
- opentriad : Open triads
- simmelian : Simmelian triads
- simmelianties : Ties in simmelian triads
- transitive : Transitive triads
- transitiveties : Transitive ties
- transitiveties : Transitive ties
- transitiveweights : Transitive weights
- triadcensus : Triad census
- triangle : Triangles
- tripercent : Triangle percentage
- ttriple : Transitive triples
- ttriad : Transitive triples

### bipartite

- b1concurrent : Concurrent node count for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network
- b1degrange : Degree range for the first mode in a bipartite (a.k.a. two-mode) network
- b1degree : Degree for the first mode in a bipartite (aka two-mode) network
- b1dsp : Dyadwise shared partners for dyads in the first bipartition
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1factor : Factor attribute effect for the first mode in a bipartite (aka two-mode) network
- b1mindegree : Minimum degree for the first mode in a bipartite (aka two-mode) network
- b1nodematch : Nodal attribute-based homophily effect for the first mode in a bipartite (aka two-mode) network
- b1sociality : Degree
- b1sociality : Degree
- b1star : k-Stars for the first mode in a bipartite (aka two-mode) network
- b1starmix : Mixing matrix for k-stars centered on the first mode of a bipartite network
- b1twostar : Two-star census for central nodes centered on the first mode of a bipartite network
- b2concurrent : Concurrent node count for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2cov : Main effect of a covariate for the second mode in a bipartite (aka two-mode) network
- b2degrange : Degree range for the second mode in a bipartite (a.k.a. two-mode) network
- b2degree : Degree for the second mode in a bipartite (aka two-mode) network
- b2dsp : Dyadwise shared partners for dyads in the second bipartition
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2factor : Factor attribute effect for the second mode in a bipartite (aka two-mode) network
- b2mindegree : Minimum degree for the second mode in a bipartite (aka two-mode) network
- b2nodematch : Nodal attribute-based homophily effect for the second mode in a bipartite (aka two-mode) network
- b2sociality : Degree
- b2sociality : Degree
- b2star : k-Stars for the second mode in a bipartite (aka two-mode) network
- b2starmix : Mixing matrix for k-stars centered on the second mode of a bipartite network
- b2twostar : Two-star census for central nodes centered on the second mode of a bipartite network
- coincidence : Coincident node count for the second mode in a bipartite (aka two-mode) network
- diff : Difference
- gwb1degree : Geometrically weighted degree distribution for the first mode in a bipartite (aka two-mode) network
- gwb1dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition
- gwb2degree : Geometrically weighted degree distribution for the second mode in a bipartite (aka two-mode) network
- gwb2dsp : Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition
- isolatededges : Isolated edges

### quantitative nodalattribute

- b1cov : Main effect of a covariate for the first mode in a bipartite (aka two-mode) network

### deprecated

- degreepopularity : Degree popularity (deprecated)
- idegreepopularity : In-degree popularity (deprecated)
- odegreepopularity : Out-degree popularity (deprecated)

### non-negative

- nodeisqrtcovar : Uncentered covariance of square roots of in-dyad values incident on each actor
- nodeosqrtcovar : Uncentered covariance of square roots of out-dyad values incident on each actor
- nodesqrtcovar : Covariance of square roots of dyad values incident on each actor
- transitiveweights : Transitive weights

This documentation was built with..

    sessionInfo()

    ## R version 4.0.3 RC (2020-10-02 r79292)
    ## Platform: x86_64-pc-linux-gnu (64-bit)
    ## Running under: Debian GNU/Linux bullseye/sid
    ##
    ## Matrix products: default
    ## BLAS:   /usr/lib/x86_64-linux-gnu/atlas/libblas.so.3.10.3
    ## LAPACK: /usr/lib/x86_64-linux-gnu/atlas/liblapack.so.3.10.3
    ##
    ## locale:
    ##  [1] LC_CTYPE=en_AU.UTF-8      LC_NUMERIC=C
    ##  [3] LC_TIME=en_AU.utf8        LC_COLLATE=C
    ##  [5] LC_MONETARY=en_AU.utf8    LC_MESSAGES=en_AU.UTF-8
    ##  [7] LC_PAPER=en_AU.utf8       LC_NAME=C
    ##  [9] LC_ADDRESS=C              LC_TELEPHONE=C
    ## [11] LC_MEASUREMENT=en_AU.utf8 LC_IDENTIFICATION=C
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] ergm_3.11.0    network_1.16.1
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    ## loaded via a namespace (and not attached):
    ##  [1] knitr_1.30.2         magrittr_1.5         MASS_7.3-53
    ##  [4] lattice_0.20-41      rlang_0.4.8          stringr_1.4.0
    ##  [7] tools_4.0.3          parallel_4.0.3       grid_4.0.3
    ## [10] lpSolve_5.6.15       rle_0.9.2            xfun_0.18
    ## [13] coda_0.19-4          htmltools_0.5.0      ellipsis_0.3.1
    ## [16] yaml_2.2.1           digest_0.6.25        tibble_3.0.4
    ## [19] lifecycle_0.2.0      crayon_1.3.4         Matrix_1.2-18
    ## [22] purrr_0.3.4          vctrs_0.3.4          trust_0.1-8
    ## [25] robustbase_0.93-6    evaluate_0.14        rmarkdown_2.4
    ## [28] statnet.common_4.4.1 stringi_1.5.3        DEoptimR_1.0-8
    ## [31] compiler_4.0.3       pillar_1.4.6         pkgconfig_2.0.3