DUNCAN J. WATTS AND STEVEN H. STROGATZ: Collective dynamics of=20
'small-world' networks
Nature 393, 440-442 (1998) Letters to Nature
http://www.nature.com/server-java/Propub/nature/393440A0.abs_frameset
4 June 1998
Nature 393, 440 - 442 (1998) =A9 Macmillan Publishers Ltd.
Collective dynamics of 'small-world' networks
DUNCAN J. WATTS AND STEVEN H. STROGATZ
Networks of coupled dynamical systems have been used to model=20
biological oscillators, Josephson junction arrays, excitable media,=20
neural networks, spatial games, genetic control networks and many=20
other self-organizing systems. Ordinarily, the connection topology is=20
assumed to be either completely regular or completely random. But=20
many biological, technological and social networks lie somewhere=20
between these two extremes. Here we explore simple models of networks=20
that can be tuned through this middle ground: regular networks=20
'rewired' to introduce increasing amounts of disorder. We find that=20
these systems can be highly clustered, like regular lattices, yet=20
have small characteristic path lengths, like random graphs. We call=20
them 'small-world' networks, by analogy with the small-world=20
phenomenon (popularly known as six degrees of separation). The neural=20
network of the worm Caenorhabditis elegans, the power grid of the=20
western United States, and the collaboration graph of film actors are=20
shown to be small-world networks. Models of dynamical systems with=20
small-world coupling display enhanced signal-propagation speed,=20
computational power, and synchronizability. In particular, infectious=20
diseases spread more easily in small-world networks than in regular=20
lattices.