rgnm: 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)

Value

A matrix or array containing the drawn adjacency matrices

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?

Author

Carter T. Butts buttsc@uci.edu

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

$$ p(G=g|N,M) = \left( {E_m \atop M} \right)^{-1} $$

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.

References

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

Examples

Run this code

#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))

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