# UniformGraphDistribution

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

# Examples

open allclose all

## 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 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_2024_uniformgraphdistribution, author="Wolfram Research", title="{UniformGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/UniformGraphDistribution.html}", note=[Accessed: 13-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_uniformgraphdistribution, organization={Wolfram Research}, title={UniformGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/UniformGraphDistribution.html}, note=[Accessed: 13-August-2024 ]}