sna (version 2.6)

# rgraph: Generate Bernoulli Random Graphs

## Description

`rgraph` generates random draws from a Bernoulli graph distribution, with various parameters for controlling the nature of the data so generated.

## Usage

```rgraph(n, m=1, tprob=0.5, mode="digraph", diag=FALSE, replace=FALSE,
tielist=NULL, return.as.edgelist=FALSE)```

## Arguments

n

The size of the vertex set (|V(G)|) for the random graphs

m

The number of graphs to generate

tprob

Information regarding tie (edge) probabilities; see below

mode

``digraph'' for directed data, ``graph'' for undirected data

diag

Should the diagonal entries (loops) be set to zero?

replace

Sample with or without replacement from a tie list (ignored if `tielist==NULL`

tielist

A vector of edge values, from which the new graphs should be bootstrapped

return.as.edgelist

logical; should the resulting graphs be returned in edgelist form?

A graph stack

## Details

`rgraph` is a reasonably versatile routine for generating random network data. The graphs so generated are either Bernoulli graphs (graphs in which each edge is a Bernoulli trial, independent conditional on the Bernoulli parameters), or are bootstrapped from a user-provided edge distribution (very handy for CUG tests). In the latter case, edge data should be provided using the `tielist` argument; the exact form taken by the data is irrelevant, so long as it can be coerced to a vector. In the former case, Bernoulli graph probabilities are set by the `tprob` argument as follows:

1. If `tprob` contains a single number, this number is used as the probability of all edges.

2. If `tprob` contains a vector, each entry is assumed to correspond to a separate graph (in order). Thus, each entry is used as the probability of all edges within its corresponding graph.

3. If `tprob` contains a matrix, then each entry is assumed to correspond to a separate edge. Thus, each entry is used as the probability of its associated edge in each graph which is generated.

4. Finally, if `tprob` contains a three-dimensional array, then each entry is assumed to correspond to a particular edge in a particular graph, and is used as the associated probability parameter.

Finally, note that `rgraph` will symmetrize all generated networks if `mode` is set to ``graph'' by copying down the upper triangle. The lower half of `tprob`, where applicable, must still be specified, however.

## References

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

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

`rmperm`, `rgnm`, `rguman`

## Examples

```# NOT RUN {
#Generate three graphs with different densities
g<-rgraph(10,3,tprob=c(0.1,0.9,0.5))

#Generate from a matrix of Bernoulli parameters
g.p<-matrix(runif(25,0,1),nrow=5)
g<-rgraph(5,2,tprob=g.p)
# }
```