networkx.generators.random_graphs.newman_watts_strogatz_graph¶

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

Return a Newman–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 adding a new edge for each edge. seed (int, optional) – The seed for the random number generator (the default is None).

Notes

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.