Collective Dynamics of Small-World Networks — Interactive Demo

Watts & Strogatz (1998) started from a regular ring lattice, where every node connects only to its nearest neighbors — highly clustered, but far apart (many hops between distant nodes). They then rewired each local edge to a random node with probability p. At p = 1 the network is essentially random: short paths, but almost no local clustering. The surprise was in between — even a tiny amount of rewiring (small p) collapses the average path length almost to the random-graph level, while the clustering coefficient barely drops. A network can be both highly clustered and a "small world" at the same time.

Drag the slider to rewire the illustrative ring on the left, and watch where that p lands on the reference curve on the right (computed once from a larger N = 400 network) — the same curve shape as the paper's Figure 2.