watts_strogatz_graph(n, k, p, seed=None)
First create a ring over $n$ nodes . 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 $w$.
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 in connected_watts_strogatz_graph
.
The number of nodes
Each node is joined with its k nearest neighbors in a ring topology.
The probability of rewiring each edge
Indicator of random number generation state. See Randomness<randomness>
.
Returns a Watts–Strogatz small-world graph.
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.generators.random_graphs.connected_watts_strogatz_graph
networkx.generators.random_graphs.newman_watts_strogatz_graph
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them