networkx.generators.random_graphs.newman_watts_strogatz_graph¶

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

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

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.