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).

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    $\begingroup$ Of course; there are lots of them! What other properties do you want? A simple example: Generate the lower diagonal entries as iid Bernoulli random variables with a small probability of success and "symmetrize". $\endgroup$
    – cardinal
    Commented Jul 6, 2012 at 13:37
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    $\begingroup$ OK, I walked into that one. I've added some clarification. $\endgroup$
    – Chris
    Commented Jul 6, 2012 at 13:50
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    $\begingroup$ Is the "distance" an actual metric or just some pairwise "affinity" that, say, gets threshold to produce the edges? $\endgroup$
    – cardinal
    Commented Jul 6, 2012 at 14:00
  • $\begingroup$ In the simplest case, the distance is an actual distance (e.g., measurable in mm). $\endgroup$
    – Chris
    Commented Jul 6, 2012 at 14:02
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    $\begingroup$ This sounds like the random dot-product model. $\endgroup$
    – whuber
    Commented Jul 6, 2012 at 14:36


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