This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# WattsStrogatzGraphDistribution

 WattsStrogatzGraphDistribution represents the Watts-Strogatz graph distribution for n-vertex graphs with rewiring probability p. WattsStrogatzGraphDistributionrepresents the Watts-Strogatz graph distribution for n-vertex graphs with rewiring probability p starting from a 2k-regular graph.
Generate a Watts-Strogatz graph with 50 vertices and 0.05 rewiring probability:
With higher rewiring probability, more shortcuts are added:
Generate several graphs:
Generate a Watts-Strogatz graph with 50 vertices and 0.05 rewiring probability:
 Out[1]=

With higher rewiring probability, more shortcuts are added:
 Out[1]=

Generate several graphs:
 Out[1]=
 Applications   (2)
The mean distance decreases quickly with rewiring probability:
The graph diameter increases slowly for a Watts-Strogatz graph:
Watts-Strogatz graphs are simple:
And connected:
Watts-Strogatz graphs are nearly regular for small p and uniformly random for large p:
Vertex degree distribution shifts from a point distribution to a binomial distribution:
Randomly colored vertices:
New in 8