Critical behavior of propagation on small-world networks

Details Critical behavior of propagation on small-world networks Critical behavior of propagation on small-world networks

2001-05-30

arxiv.org/abs/cond-mat/0105596v2

Physics

Condensed Matter

Statistical Mechanics

More definitive version. Text modified, 1 figure added

Scientific paper

10.1103/PhysRevE.64.050901

We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a regime where the rumor "dies" in a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the whole population. Critical exponents are evaluated, and the dependence of the critical randomness with the network connectivity is studied. The behavior of this system as a function of the small-network randomness bears noticeable similarities with an epidemiological model reported recently [M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the respective dynamical rules.

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