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triad.census {igraph}

Triad census, subgraphs with three vertices
Package: 
igraph
Version: 
0.6.5-2

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.

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 graph.motifs.

Values

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

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, graph.motifs for the underlying implementation.

Examples

g <- erdos.renyi.game(15, 45, type="gnm", dir=TRUE)
triad.census(g)

Author(s)

Gabor Csardi csardi.gabor@gmail.com

Documentation reproduced from package igraph, version 0.6.5-2. License: GPL (>= 2)