# WattsStrogatzGraphDistribution

represents the WattsStrogatz graph distribution for n-vertex graphs with rewiring probability p.

represents the WattsStrogatz graph distribution for n-vertex graphs with rewiring probability p starting from a 2k-regular graph.

# Examples

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## Basic Examples(2)

Generate a pseudorandom graph:

GlobalClusteringCoefficient as a function of rewiring probability:

## Scope(3)

Generate simple undirected graphs:

Generate a set of pseudorandom graphs:

Compute probabilities and statistical properties:

## Applications(3)

The Western States Power Grid can be modeled with WattsStrogatzGraphDistribution:

The model captures the small-world characteristics of the empirical network, with short mean graph distance and high clustering:

A social network in a village of 100 people where the average number of relations per person is 20 can be modeled using a WattsStrogatzGraphDistribution. Find the expected number of relations for the least-connected person:

The expected number of relations for the least-connected person:

Expected degree separation:

This represents a simplified model for the spread of an infectious disease in a social network. The disease spreads in each step with probability 0.4 from infected individuals to some of their susceptible neighbors, while infected individuals recover and become immune:

Simulate an infection and find infected persons:

Highlight infected persons:

The fraction of infected persons as a function of the transmission probability:

## Properties & Relations(5)

Distribution of the number of vertices:

Distribution of the number of edges:

Distribution of the vertex degree:

Approximate with a sum of BinomialDistribution and PoissonDistribution:

The mean distance decreases quickly as the rewiring probability increases:

The clustering coefficient decreases slowly:

is a 2k-regular graph:

For n2k it is (n-1)-regular:

## Neat Examples(1)

Randomly colored vertices:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_wattsstrogatzgraphdistribution, author="Wolfram Research", title="{WattsStrogatzGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}", note=[Accessed: 29-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_wattsstrogatzgraphdistribution, organization={Wolfram Research}, title={WattsStrogatzGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}, note=[Accessed: 29-May-2023 ]}