Small-world network

A small-world network is a specific kind of network (to be more precise a special kind of a complex network) in which the distribution of connectivity is not confined to a certain scale, and where every node can be reached from every other by a small number of hops or steps. It 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. Duncan J. Watts and Steven Strogatz (1998) have identified it as a general feature of certain networks and propose that a similar phenomenon can occur in any network.

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

If the clustering coefficient is significantly higher than would be expected for a random network, and the mean shortest-path length is lower, 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 shortest-path length from one person to any other is possibly very short.