triad_census: Triad census, subgraphs with three vertices

Description

This function counts the different subgraphs of three vertices in a graph.

Usage

triad_census(graph)

Arguments

graph

The input graph, it should be directed. An undirected graph
results a warning, and undefined results.

Value

A numeric vector, the subgraph counts, in the order given in the
above description.

Details

Triad census was defined by David and Leinhardt (see References below).
Every triple of vertices (A, B, C) are classified into the 16 possible
states:

003

A,B,C, the empty graph.

012

A->B, C,
the graph with a single directed edge.

102

A<->B, C, the graph with
a mutual connection between two vertices.

021D

A<-B->C, the
out-star.

021U

A->B<-C, the in-star.

021C

A->B->C, directed
line.

111D

A<->B<-C.

111U

A<->B->C.

030T

A->B<-C,
A->C.

030C

A<-B<-C, A->C.

201

A<->B<->C.

120D

A<-B->C, A<->C.

120U

A->B<-C, A<->C.

120C

A->B->C, A<->C.

210

A->B<->C, A<->C.

300

A<->B<->C, A<->C, the complete graph.

This functions uses the RANDESU motif finder algorithm to find and count the
subgraphs, see motifs.

References

See also Davis, J.A. and Leinhardt, S. (1972). The Structure
of Positive Interpersonal Relations in Small Groups. In J. Berger (Ed.),
Sociological Theories in Progress, Volume 2, 218-251. Boston: Houghton
Mifflin.

See Also

dyad_census for classifying binary relationships,
motifs for the underlying implementation.