Watts-Strogatz Small-World Network

Rewiring probability controls the transition from lattice to random graph
30
4
0.10
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Clustering C
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Avg Path L
Regular Lattice
The Watts-Strogatz model (1998) interpolates between a regular ring lattice and a random graph by rewiring each edge with probability β. At small β, the network retains high clustering (like a lattice) while path length drops dramatically — the hallmark of a small world. Real social networks, the brain, and the power grid all live in this sweet spot.