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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.

Suggested Citation

  • Cristopher Moore & M. E. J. Newman, 2000. "Exact Solution of Site and Bond Percolation on Small-World Networks," Working Papers 00-01-007, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:00-01-007
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    References listed on IDEAS

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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, February.
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    Cited by:

    1. Shriram Ashok Kumar & Maliha Tasnim & Zohvin Singh Basnyat & Faezeh Karimi & Kaveh Khalilpour, 2022. "Resilience Analysis of Australian Electricity and Gas Transmission Networks," Sustainability, MDPI, vol. 14(6), pages 1-20, March.
    2. Sam Langfield & Kimmo Soramäki, 2016. "Interbank Exposure Networks," Computational Economics, Springer;Society for Computational Economics, vol. 47(1), pages 3-17, January.
    3. Claudio J. Tessone, "undated". "Collective behaviour induced by network volatility," Working Papers ETH-RC-14-010, ETH Zurich, Chair of Systems Design.
    4. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. repec:plo:pone00:0203894 is not listed on IDEAS
    6. Mitra, Tushar & Hassan, Md. Kamrul, 2022. "A weighted planar stochastic lattice with scale-free, small-world and multifractal properties," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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    Keywords

    Small world; disease spreading; epidemics; social networks.;
    All these keywords.

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