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.

##### 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.

dyad.census for classifying binary relationships, graph.motifs for the underlying implementation.
g <- erdos.renyi.game(15, 45, type="gnm", dir=TRUE)
triad.census(g)