WOLFRAM

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.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

Generate a pseudorandom graph:

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GlobalClusteringCoefficient as a function of rewiring probability:

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Scope  (3)Survey of the scope of standard use cases

Generate simple undirected graphs:

Out[1]=1

Generate a set of pseudorandom graphs:

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Compute probabilities and statistical properties:

Out[2]=2

Applications  (3)Sample problems that can be solved with this function

The Western States Power Grid can be modeled with WattsStrogatzGraphDistribution:

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

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Out[4]=4

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:

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

Out[3]=3

Expected degree separation:

Out[4]=4

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:

Out[1]=1

Simulate an infection and find infected persons:

Highlight infected persons:

Out[4]=4

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

Out[6]=6

Properties & Relations  (5)Properties of the function, and connections to other functions

Distribution of the number of vertices:

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Distribution of the number of edges:

Out[1]=1

Distribution of the vertex degree:

Out[2]=2

Approximate with a sum of BinomialDistribution and PoissonDistribution:

Out[4]=4

The mean distance decreases quickly as the rewiring probability increases:

Out[1]=1

The clustering coefficient decreases slowly:

Out[2]=2

WattsStrogatzGraphDistribution[n,0,k] is a 2k-regular graph:

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Out[2]=2

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

Out[3]=3
Out[4]=4

Neat Examples  (1)Surprising or curious use cases

Randomly colored vertices:

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

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.

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

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

BibTeX

@misc{reference.wolfram_2025_wattsstrogatzgraphdistribution, author="Wolfram Research", title="{WattsStrogatzGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}", note=[Accessed: 28-February-2025 ]}

@misc{reference.wolfram_2025_wattsstrogatzgraphdistribution, author="Wolfram Research", title="{WattsStrogatzGraphDistribution}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}", note=[Accessed: 28-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_wattsstrogatzgraphdistribution, organization={Wolfram Research}, title={WattsStrogatzGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}, note=[Accessed: 28-February-2025 ]}

@online{reference.wolfram_2025_wattsstrogatzgraphdistribution, organization={Wolfram Research}, title={WattsStrogatzGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}, note=[Accessed: 28-February-2025 ]}