seed = integer or none

Seed for the random number generator. Equivalent to calling randomize(seed) immediately before invoking this function.

WattsStrogatzGraph(n,p,k,options) creates a Watts-Strogatz random graph on n vertices.

The random number generator used can be seeded using the seed option or the randomize function.

A Watts-Strogatz random graph is a circulant graph with parameters n and k in which each edge has been rewired with probability p.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{RandomGraphs}\right)\:$

$G≔\mathrm{WattsStrogatzGraph}\left(8\,0.5\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 8\; vertices\; and\; 14\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{DegreeSequence}\left(G\right)$

$\left[3\,5\,2\,3\,3\,5\,4\,3\right]$

$G≔\mathrm{WattsStrogatzGraph}\left(100\,0.25\,3\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 100\; vertices\; and\; 300\; edge(s)}$

$\mathrm{Statistics}:-\mathrm{Histogram}\left(\mathrm{DegreeSequence}\left(G\right)\right)$

$\mathrm{Statistics}:-\mathrm{Tally}\left(\mathrm{DegreeSequence}\left(G\right)\right)$

$\left[4=6\,5=22\,6=43\,7=24\,8=5\right]$

Watts, D. J.; Strogatz, S. H. (1998). "Collective dynamics of 'small-world' networks". Nature. 393 (6684): 440–442. (4 June 1998). doi:10.1038/30918. PMID 9623998.

The GraphTheory[RandomGraphs][WattsStrogatzGraph] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.