represents a uniform graph distribution on n-vertex, m-edge graphs.
Details and Options
- The sample space is all simple graphs on n vertices and m edges.
- The following options can be given:
DirectedEdges False whether to generate directed edges
- UniformGraphDistribution can be used with such functions as RandomGraph and GraphPropertyDistribution.
Examplesopen allclose all
Basic Examples (2)
By default, undirected graphs are generated:
Use DirectedEdges->True to generate directed graphs:
On a duet night at the karaoke club, 85 songs are performed by 40 guests selected randomly. Find the expected number of people who sang at least 3 songs:
Find the largest component fraction when the mean vertex degree is approximately :
Average the result over 100 runs and plot it for different numbers of vertices:
Properties & Relations (4)
Distribution of the number of vertices:
Distribution of the number of edges:
Distribution of the degree of a vertex:
The mean vertex degree is 2m/n:
Use RandomSample to simulate a UniformGraphDistribution:
Wolfram Research (2010), UniformGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/UniformGraphDistribution.html.
Wolfram Language. 2010. "UniformGraphDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UniformGraphDistribution.html.
Wolfram Language. (2010). UniformGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UniformGraphDistribution.html