# DegreeGraphDistribution

DegreeGraphDistribution[dlist]

represents a degree graph distribution with vertex degree dlist.

# Examples

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## Basic Examples(2)

Generate a pseudorandom graph:

Probability density functions of the global clustering coefficient:

## Scope(3)

Generate simple undirected graphs:

Generate a set of pseudorandom graphs:

Compute probabilities and statistical properties:

## Applications(2)

In a medical study of an outbreak of influenza, each subject reported its number of potentially contagious interactions within the group. Simulate interaction networks:

Find the probability that subject 1 has interacted with subject 2:

Analyze whether a network is drawn from a degree graph distribution:

Compare the empirical and theoretical basic properties:

The empirical and theoretical global clustering coefficient:

## Properties & Relations(7)

Distribution of the number of vertices:

Distribution of the number of edges:

Distribution of the degree of a vertex:

Probability density function:

The mean of the degree of a vertex:

The sum of the degree sequence of a graph is always even:

Degree sequences with odd total degree cannot be realized as a graph:

is a degree sequence of a simple graph iff is:

Ordered degree sequence:

Reconstruct the degree sequence without the largest degree vertex:

The graphs with the same degree sequence can be non-isomorphic:

A degree sequence with distinct degrees is realized as a graph with self-loops:

## Neat Examples(1)

Randomly colored vertices:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_degreegraphdistribution, author="Wolfram Research", title="{DegreeGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html}", note=[Accessed: 22-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_degreegraphdistribution, organization={Wolfram Research}, title={DegreeGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/DegreeGraphDistribution.html}, note=[Accessed: 22-June-2024 ]}