represents the Watts–Strogatz graph distribution for n-vertex graphs with rewiring probability p.
represents the Watts–Strogatz graph distribution for n-vertex graphs with rewiring probability p starting from a 2k-regular graph.
- WattsStrogatzGraphDistribution[n,p] is equivalent to WattsStrogatzGraphDistribution[n,p,2].
- The WattsStrogatzGraphDistribution is constructed starting from CirculantGraph[n,Range[k]] and rewiring each edge with probability p. Each edge is rewired by changing one of the vertices, making sure that no loop or multiple edge is created.
- WattsStrogatzGraphDistribution can be used with such functions as RandomGraph and GraphPropertyDistribution.
Examplesopen allclose all
Basic Examples (2)
Generate a pseudorandom graph:
GlobalClusteringCoefficient as a function of rewiring probability:
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:
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:
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:
Wolfram Research (2010), WattsStrogatzGraphDistribution, Wolfram Language function, 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.
Wolfram Language. (2010). WattsStrogatzGraphDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.html