The title says it all, really. I'm aware of the Wishart distribution for symmetric, nonnegative-definite matrix-valued random variables, and am looking for something along these lines, but for sparse symmetric, binary matrix-valued random variables. If necessary, I'm willing to forego the requirement that the matrices be sparse.
The context for this is the study of adjacency matrices for undirected graphs. In particular, “distant” vertices are unlikely to be connected, hence the sparsity (whereby “distant”, I mean dissimilarity between whatever it is that the vertices represent, measured in some suitable way).
Thanks in advance.