Warning
This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.
watts_strogatz_graph¶

watts_strogatz_graph
(n, k, p, seed=None)[source]¶ Return a Watts–Strogatz smallworld graph.
Parameters: Notes
First create a ring over
n
nodes. Then each node in the ring is joined to itsk
nearest neighbors (ork  1
neighbors ifk
is odd). Then shortcuts are created by replacing some edges as follows: for each edge(u, v)
in the underlying “n
ring withk
nearest neighbors” with probabilityp
replace it with a new edge(u, w)
with uniformly random choice of existing nodew
.In contrast with
newman_watts_strogatz_graph()
, the random rewiring does not increase the number of edges. The rewired graph is not guaranteed to be connected as inconnected_watts_strogatz_graph()
.References
[1] Duncan J. Watts and Steven H. Strogatz, Collective dynamics of smallworld networks, Nature, 393, pp. 440–442, 1998.