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Mathematica > Mathematics and Algorithms > Graphs & Networks > Constructing Graphs > UniformGraphDistribution >
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UniformGraphDistribution

UniformGraphDistribution
represents a uniform graph distribution on n-vertex, m-edge graphs.
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  • The sample space is all simple graphs on n vertices and m edges.
EXAMPLESCLOSE ALL
Basic Examples   (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:
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Click for copyable input
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Generate a random directed graph with 5 vertices and 6 edges:
In[1]:=
Click for copyable input
Out[1]=
 
Generate several graphs:
In[1]:=
Click for copyable input
Out[1]=
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:
Properties & Relations   (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:
Neat Examples   (2)
Random colored vertices:
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