WattsStrogatzGraphDistribution

WattsStrogatzGraphDistribution[n,p]

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

WattsStrogatzGraphDistribution[n,p,k]

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)

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:

WattsStrogatzGraphDistribution[n,0,k] 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: 06-July-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_wattsstrogatzgraphdistribution, organization={Wolfram Research}, title={WattsStrogatzGraphDistribution}, year={2010}, url={https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html}, note=[Accessed: 06-July-2022 ]}