Critical behavior of propagation on small-world networks
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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Cite
@article{arxiv.cond-mat/0105596,
title = {Critical behavior of propagation on small-world networks},
author = {Damian H. Zanette},
journal= {arXiv preprint arXiv:cond-mat/0105596},
year = {2009}
}
Comments
More definitive version. Text modified, 1 figure added