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networkx.generators.random_graphs.watts_strogatz_graph

watts_strogatz_graph(n, k, p, seed=None)

Returns a Watts–Strogatz small-world graph.

Parameters

• n (int) – The number of nodes

• k (int) – Each node is joined with its k nearest neighbors in a ring topology.

• p (float) – The probability of rewiring each edge

• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

See also

newman_watts_strogatz_graph(), connected_watts_strogatz_graph()

Notes

First create a ring over \(n\) nodes 1. Then each node in the ring is joined to its \(k\) nearest neighbors (or \(k - 1\) neighbors if \(k\) is odd). Then shortcuts are created by replacing some edges as follows: for each edge \((u, v)\) in the underlying “\(n\)-ring with \(k\) nearest neighbors” with probability \(p\) replace it with a new edge \((u, w)\) with uniformly random choice of existing node \(w\).

In contrast with newman_watts_strogatz_graph(), the random rewiring does not increase the number of edges. The rewired graph is not guaranteed to be connected as in connected_watts_strogatz_graph().

References

1

Duncan J. Watts and Steven H. Strogatz, Collective dynamics of small-world networks, Nature, 393, pp. 440–442, 1998.