Watts-Strogatz model

Start with regular ring lattice. Rewire each edge with probability p. Interpolates between lattice + random.

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Properties

p = 0: high clustering, high diameter. p = 1: low clustering, low diameter. Small p: high clustering + low diameter — small-world regime.

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Milgram's experiment

1967 mail-passing study estimated 6-hop average distance between random Americans.

Kleinberg's algorithmic small world

Grid + long-range edges with distribution ~1/d² → decentralized greedy routing finds targets in O(log² N) hops.