R: Triad census, subgraphs with three vertices

triad_census {igraph} | R Documentation

## Triad census, subgraphs with three vertices

### 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 `motifs`.

### Value

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

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### 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.

### Examples

    g <- sample_gnm(15, 45, directed = TRUE)
    triad_census(g)

[Package igraph version 1.3.2 Index]