# triad.census {igraph}

### 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)

Documentation reproduced from package igraph, version 0.7.0. License: GPL (>= 2)