(a dirichlet so parameterized would necessarily be varying degrees flat or uniform over all the candidate models, though… I do wonder if it would be possible to specify a distribution over the network with parameters capturing both central tendency and dispersion? Maybe something where you have a discrete “mean” model node and mass proportional to, say, the minimum number of edges some other node is away from it? The only other context I’m really familiar with in which probability distributions are defined over graphs is phylogenetics, using e.g. variations on the birth-death process, but that’s specifying distributions over graphs and not nodes in a fixed graph)

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