Exact Solution of Site and Bond Percolation on Small-World Networks
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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| Length: | |
| Date of creation: | Jan 2000 |
| Date of revision: | |
| Handle: | RePEc:wop:safiwp:00-01-007 |
| Contact details of provider: | Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501 Web page: http://www.santafe.edu/sfi/publications/working-papers.html More information through EDIRC
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References listed on IDEAS
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- E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
- 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.
- 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.
- Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
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