Small-world network

A small-world network is a generalisation of the small-world phenomenon, as in the phenomenon where we suddenly burst out "It's a small world" when we meet a stranger who we find is linked by a mutual acquaintance.

The small-world phenomenon applies to social networks. Watts and Strogatz (1998) argue that a similar phenomenon can apply to any network.

They propose that we can measure whether a network is a small world or not according to two graph (mathematics) measurements of the network: clustering coefficient and mean-shortest path length (also called closeness).

If the both the clustering coefficient and closeness are significantly higher than would be expected for a random network, then the network is a small world. We can see how this works for the small-world phenomenon: most people have a relatively small circle of friends who generally all know each other (highly clustered), but the closeness between people over the whole world is relatively high, with possibly only six steps between any one person and any other in the entire world.