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Critical behavior of propagation on small-world networks

Damian H. Zanette
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Abstract

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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Damian H. Zanette. 2001-06-04. Critical behavior of propagation on small-world networks. https://doi.org/10.1103/physreve.64.050901

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