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Exact Solution of Site and Bond Percolation on Small-World Networks

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    Abstract

    We study percolation on small-world networks, which has been proposed as a simple model of the propagation of disease. The occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively. We give an exact solution of the model for both site and bond percolation, including the position of the percolation transition at which epidemic behavior sets in, the values of the two critical exponents governing this transition, and the mean and variance of the distribution of cluster sizes (disease outbreaks) below the transition.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 00-01-007.

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    Date of creation: Jan 2000
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    Handle: RePEc:wop:safiwp:00-01-007

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    Keywords: Small world; disease spreading; epidemics; social networks.;

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    1. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    2. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    3. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
    4. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 13(3), pages 547-560, 02.
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    Cited by:
    1. Claudio J. Tessone, . "Collective behaviour induced by network volatility," Working Papers ETH-RC-14-010, ETH Zurich, Chair of Systems Design.

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