Triad census, subgraphs with three vertices

This function counts the different induced 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.

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