Small-World Networks

Watts-Strogatz model: from regular ring to random graph

40
4
β = 0.10
Regular edges
Rewired (shortcut)
Selected node
BFS layer
Avg Path Length L
Clustering C
L / L_regular
C / C_regular
Shortcuts

The Watts-Strogatz (1998) model starts with a regular ring lattice where each node connects to its k nearest neighbors, then rewires each edge with probability β. Even a small β creates shortcuts that collapse average path length while preserving high clustering — the hallmark of real social networks, power grids, and neural circuits. Click any node to see its BFS layers. The sweet spot β ≈ 0.01–0.1 gives the small-world regime: L ≈ L_random, C ≈ C_regular.