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watts_strogatz_graph(n, k, p, seed=None)[source]

Return a Watts–Strogatz small-world graph.

  • 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 (int, optional) – Seed for random number generator (default=None)


First create a ring over n nodes. 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().


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