Small-World Network Lab
Watts and Strogatz asked in 1998 how a network can be highly clustered like a village yet traversable in a few hops like the whole world — and answered with one parameter. Start from a ring lattice where every node knows its k nearest neighbours, then rewire each edge to a random target with probability p. This lab draws the network live on a circle as you drag N, k and a logarithmic p slider, and sweeps p to plot the two classic curves: normalised average path length L(p)/L(0) and clustering C(p)/C(0). Between them lies the small-world regime, where a handful of shortcuts has already collapsed the path length while clustering barely moved. A six-degrees demo picks two nodes and highlights the BFS shortest path between them — watch it shrink from N/2k hops to a handful as p grows.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The signature result: path length falls almost immediately (a few shortcuts serve the whole network) while clustering needs many rewirings to erode — the gap between the two curves is the small-world regime.
- At p = 0 the ring lattice has L ≈ N/2k and high clustering; at p = 1 the graph is essentially random with L ≈ ln N / ln k and negligible clustering.
- Milgram’s 1967 letter experiment found chains of about six acquaintances between strangers — the “six degrees of separation” that small-world topology explains.
- Real networks — power grids, neural wiring, film-actor collaborations, the web — sit in the small-world regime, which speeds both information spread and epidemics.
- Runs 100% in your browser — simulations are computed locally on your device.
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