R: Draw Density-Conditioned Random Graphs

rgnm {sna} | R Documentation

## Draw Density-Conditioned Random Graphs

### Description

`rgnm` generates random draws from a density-conditioned uniform random graph distribution.

### Usage

    rgnm(n, nv, m, mode = "digraph", diag = FALSE,
        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.
`m` | the number of edges on which to condition.
`mode` | `"digraph"` for directed graphs, or `"graph"` for undirected graphs.
`diag` | logical; should loops be allowed?
`return.as.edgelist` | logical; should the resulting graphs be returned in edgelist form?

### Details

`rgnm` returns draws from the density-conditioned uniform random graph first popularized by the famous work of Erdos and Renyi (the G(N,M) process). In particular, the pmf of a G(N,M) process is given by

p(G=g|N,M) = 1/Choose(E_m,M)

where E_m is the maximum number of edges in the graph. (E_m is equal to `nv*(nv-diag)/(1+(mode=="graph"))`.)

The G(N,M) process is one of several process which are used as baseline models of social structure. Other well-known baseline models include the Bernoulli graph (the G(N,p) model of Erdos and Renyi) and the U|MAN model of dyadic independence. These are implemented within `sna` as `rgraph` and `rgnm`, respectively.

### 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

Erdos, P. and Renyi, A. (1960). “On the Evolution of Random Graphs.” Public Mathematical Institute of Hungary Academy of Sciences, 5:17-61.

### See Also

`rgraph`, `rguman`

### Examples

    #Draw 5 random graphs of order 10
    all(gden(rgnm(5,10,9,mode="graph"))==0.2) #Density 0.2
    all(gden(rgnm(5,10,9))==0.1)              #Density 0.1

    #Plot a random graph
    gplot(rgnm(1,10,20))

[Package sna version 2.7 Index]