This function counts the different induced subgraphs of three vertices in a graph.
Arguments
- graph
The input graph, it should be directed. An undirected graph results a warning, and undefined results.
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.
Author
Gabor Csardi csardi.gabor@gmail.com
Examples
g <- sample_gnm(15, 45, directed = TRUE)
triad_census(g)
#> [1] 90 198 21 20 21 57 11 15 12 5 0 2 1 2 0 0