R: Draw Dyad Census-Conditioned Random Graphs

rguman {sna} | R Documentation

## Draw Dyad Census-Conditioned Random Graphs

### Description

`rguman` generates random draws from a dyad census-conditioned uniform random graph distribution.

### Usage

    rguman(n, nv, mut = 0.25, asym = 0.5, null = 0.25,
        method = c("probability", "exact"), return.as.edgelist = FALSE)

### Arguments

`n` | the number of graphs to generate.
`nv` | the size of the vertex set (|V(G)|) for the random graphs.
`mut` | if `method=="probability"`, the probability of obtaining a mutual dyad; otherwise, the number of mutual dyads.
`asym` | if `method=="probability"`, the probability of obtaining an asymmetric dyad; otherwise, the number of asymmetric dyads.
`null` | if `method=="probability"`, the probability of obtaining a null dyad; otherwise, the number of null dyads.
`method` | the generation method to use. `"probability"` results in a multinomial dyad distribution (conditional on the underlying rates), while `"exact"` results in a uniform draw conditional on the exact dyad distribution.
`return.as.edgelist` | logical; should the resulting graphs be returned in edgelist form?

### Details

A simple generalization of the Erdos-Renyi family, the U|MAN distributions are uniform on the set of graphs, conditional on order (size) and the dyad census. As with the E-R case, there are two U|MAN variants. The first (corresponding to `method=="probability"`) takes dyad states as independent multinomials with parameters m (for mutuals), a (for asymmetrics), and n (for nulls). The resulting pmf is then

p(G=g|m,a,n) = (M+A+N)!/(M!A!N!) m^M a^A n^N,

where M, A, and N are realized counts of mutual, asymmetric, and null dyads, respectively. (See `dyad.census` for an explication of dyad types.)

The second U|MAN variant is selected by `method=="exact"`, and places equal mass on all graphs having the specified (exact) dyad census. The corresponding pmf is

p(G=g|M,A,N) = M!A!N!/(M+A+N)!.

U|MAN graphs provide a natural baseline model for networks which are constrained by size, density, and reciprocity. In this way, they provide a bridge between edgewise models (e.g., the E-R family) and models with higher order dependence (e.g., the Markov graphs).

### Value

A matrix or array containing the drawn adjacency matrices

### Note

The famous mathematicians referenced in this man page now have misspelled names, due to R's difficulty with accent marks.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Holland, P.W. and Leinhardt, S. (1976). “Local Structure in Social Networks.” In D. Heise (Ed.), Sociological Methodology, pp 1-45. San Francisco: Jossey-Bass.

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

### See Also

`rgraph`, `rgnm`, `dyad.census`

### Examples

    #Show some examples of extreme U|MAN graphs
    gplot(rguman(1,10,mut=45,asym=0,null=0,method="exact")) #Clique
    gplot(rguman(1,10,mut=0,asym=45,null=0,method="exact")) #Tournament
    gplot(rguman(1,10,mut=0,asym=0,null=45,method="exact")) #Empty

    #Draw a sample of multinomial U|MAN graphs
    g<-rguman(5,10,mut=0.15,asym=0.05,null=0.8)

    #Examine the dyad census
    dyad.census(g)

[Package sna version 2.5 Index]