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

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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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
Handle: RePEc:wop:safiwp:00-01-007
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Web page: http://www.santafe.edu/sfi/publications/working-papers.html

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

This paper has been announced in the following NEP Reports:

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  1. 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.
  2. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
  3. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, 02.
  4. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
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Cited by:

  1. Claudio J. Tessone, "undated". "Collective behaviour induced by network volatility," Working Papers ETH-RC-14-010, ETH Zurich, Chair of Systems Design.
  2. Sam Langfield & Kimmo Soramäki, 2016. "Interbank Exposure Networks," Computational Economics, Springer;Society for Computational Economics, vol. 47(1), pages 3-17, January.

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