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

Returns a Newman–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 adding a new edge for each edge.
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.


First create a ring over \(n\) nodes [1]. Then each node in the ring is connected with its \(k\) nearest neighbors (or \(k - 1\) neighbors if \(k\) is odd). Then shortcuts are created by adding new edges as follows: for each edge \((u, v)\) in the underlying “\(n\)-ring with \(k\) nearest neighbors” with probability \(p\) add a new edge \((u, w)\) with randomly-chosen existing node \(w\). In contrast with watts_strogatz_graph(), no edges are removed.


[1]M. E. J. Newman and D. J. Watts, Renormalization group analysis of the small-world network model, Physics Letters A, 263, 341, 1999. https://doi.org/10.1016/S0375-9601(99)00757-4