UniformGraphDistribution

UniformGraphDistribution[n,m]

represents a uniform graph distribution on n-vertex, m-edge graphs.

Details and Options

Examples

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Basic Examples  (2)

Generate a pseudorandom graph:

Probability density functions of the degree of a vertex:

Scope  (4)

Generate simple undirected graphs:

Simple directed graphs:

Generate a set of pseudorandom graphs:

Compute probabilities and statistical properties:

Options  (2)

DirectedEdges  (2)

By default, undirected graphs are generated:

Use DirectedEdges->True to generate directed graphs:

Applications  (2)

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:

Probability density function:

The mean vertex degree is 2m/n:

Use RandomSample to simulate a UniformGraphDistribution:

Neat Examples  (1)

Randomly colored vertices:

Wolfram Research (2010), UniformGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/UniformGraphDistribution.html.

Text

Wolfram Research (2010), UniformGraphDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/UniformGraphDistribution.html.

CMS

Wolfram Language. 2010. "UniformGraphDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UniformGraphDistribution.html.

APA

Wolfram Language. (2010). UniformGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UniformGraphDistribution.html

BibTeX

@misc{reference.wolfram_2022_uniformgraphdistribution, author="Wolfram Research", title="{UniformGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/UniformGraphDistribution.html}", note=[Accessed: 27-September-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_uniformgraphdistribution, organization={Wolfram Research}, title={UniformGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/UniformGraphDistribution.html}, note=[Accessed: 27-September-2022 ]}