Critical behavior of propagation on small-world networks

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Abstract
We show that an epidemic-like model, which can be interpreted as the propagation of a rumor or a fashion trait, 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. As a function of the small-network randomness, this system shows noticeable similarities with an epidemiological model reported very recently (M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)), in spite of the substantial differences in the respective dynamics.

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