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What is the difference between a GraphDistribution and a Distribution? I would like to make a GraphDistribution out of the ZipfDistribution and build RandomGraphs[]'s from that. i.e. is it possible to roll your own GraphDistributions?

data = EdgeCount /@ 
   RandomGraph[BernoulliGraphDistribution[6, 0.4], 10^3];
Show[Histogram[data, Automatic, "PDF"],
 DiscretePlot[PDF[BinomialDistribution[15, 0.4], m], {m, 0, 15}, 
  Joined -> True]]

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