triad.census

0th

Percentile

Triad census, subgraphs with three vertices

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

Keywords
graphs
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.}

Value

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

concept

Triad census

code

graph.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, graph.motifs for the underlying implementation.

Aliases
  • triad.census
Examples
g <- erdos.renyi.game(15, 45, type="gnm", dir=TRUE)
triad.census(g)
Documentation reproduced from package igraph, version 0.5.5-3, License: GPL (>= 2)

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