watts_strogatz_graph(n, k, p, seed=None)¶
Returns a Watts–Strogatz small-world graph.
n (int) – The number of nodes
k (int) – Each node is joined with its
knearest 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.
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 \(w\).
Duncan J. Watts and Steven H. Strogatz, Collective dynamics of small-world networks, Nature, 393, pp. 440–442, 1998.