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 than would be expected for a regular 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 shortest-path length from one person to any other is possibly very short.
See also
References
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- Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature 393, 440--442 (4 June 1998).