One of the key metrics in the small-world model is the average path length, for individuals and for the network overall. A good score for an individual means that he/she is close to all of the others in the network -- they can reach others quickly without going through too many intermediaries. A good score for the whole network indicates that everyone can reach everyone else easily and quickly. The shorter the information paths for everyone, the quicker the information arrives and the less distorted it is when it arrives. Another benefit of multiple short paths is that most members of the network have good visibility into what is happening in other parts of the network -- a greater awareness. They have wide reach, a broad network horizon, which is useful for combining key pieces of distributed intelligence into insights and patterns. In an environment where it is difficult to distinguish signal from noise, it is important to have many perspectives involved in the sense-making process.

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games11, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.