Abstract
Networks of coupled dynamical systems have been used to model biological
oscillators, Josephson junction arrays, excitable media, neural networks,
spatial games, 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.
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