This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# UniformGraphDistribution

 UniformGraphDistribution represents a uniform graph distribution on n-vertex, m-edge graphs.
• The sample space is all simple graphs on n vertices and m edges.
Generate a random undirected graph with 5 vertices and 6 edges:
Generate a random directed graph with 5 vertices and 6 edges:
Generate several graphs:
Generate a random undirected graph with 5 vertices and 6 edges:
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Generate a random directed graph with 5 vertices and 6 edges:
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Generate several graphs:
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 Applications   (1)
Find the largest component fraction when the mean vertex degree is :
Average the result over 100 runs and plot it for different numbers of vertices:
A uniform graph can be generated by selecting m edges from the complete graph of size n:
The vertex degree for follows BinomialDistribution:
The mean and standard variance:
Compare data to distribution cases:
Random colored vertices:
New in 8