R: Compute the Davis and Leinhardt Triad Census

triad.census {sna} | R Documentation

## Compute the Davis and Leinhardt Triad Census

### Description

`triad.census` returns the Davis and Leinhardt triad census of the elements of `dat` indicated by `g`.

### Usage

    triad.census(dat, g=NULL, mode = c("digraph", "graph"))

### Arguments

`dat` | a graph or graph stack.
`g` | the elements of `dat` to process.
`mode` | string indicating the directedness of edges; `"digraph"` implies a directed structure, whereas `"graph"` implies an undirected structure.

### Details

The Davis and Leinhardt triad census consists of a classification of all directed triads into one of 16 different categories; the resulting distribution can be compared against various null models to test for the presence of configural biases (e.g., transitivity bias). `triad.census` is a front end for the `triad.classify` routine, performing the classification for all triads within the selected graphs. The results are placed in the order indicated by the column names; this is the same order as presented in the `triad.classify` documentation, to which the reader is referred for additional details.

In the undirected case, the triad census reduces to four states (based on the number of edges in each triad. Where `mode=="graph"`, this is returned instead.

Compare `triad.census` to `dyad.census`, the dyadic equivalent.

### Value

A matrix whose 16 columns contain the counts of triads by class for each graph, in the directed case. In the undirected case, only 4 columns are used.

### Warning

Valued data may cause strange behavior with this routine. Dichotomize the data first.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

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.

Wasserman, S., and Faust, K. (1994). “Social Network Analysis: Methods and Applications.” Cambridge: Cambridge University Press.

### See Also

`triad.classify`, `dyad.census`, `kcycle.census`, `kpath.census`, `gtrans`

### Examples

    #Generate a triad census of random data with varying densities
    triad.census(rgraph(15,5,tprob=c(0.1,0.25,0.5,0.75,0.9)))

[Package sna version 2.6 Index]