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networkx.generators.random_graphs.connected_watts_strogatz_graph

connected_watts_strogatz_graph(n, k, p, tries=100, seed=None)

Returns a connected Watts–Strogatz small-world graph.

Attempts to generate a connected graph by repeated generation of Watts–Strogatz small-world graphs. An exception is raised if the maximum number of tries is exceeded.

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 rewiring each edge
• tries (int) – Number of attempts to generate a connected graph.
• 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 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 $w$. The entire process is repeated until a connected graph results.

See also

newman_watts_strogatz_graph(), watts_strogatz_graph()

References

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