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Legacy Documentation

Mathematica 8 (2010)

This is documentation for Mathematica 8, which was
based on an earlier version of Wolfram Language.
View current documentation (Version 14.3)

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.
(3)
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:
Out[1]=
Generate a random directed graph with 5 vertices and 6 edges:
Out[1]=
Generate several graphs:
Out[1]=
(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:
(2)
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:
(2)
Random colored vertices:
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