Exact solution of site and bond percolation on small-world networks

Details Exact solution of site and bond percolation on small-world networks Exact solution of site and bond percolation on small-world networks

2000-01-26

arxiv.org/abs/cond-mat/0001393v1

Phys. Rev. E 62, 7059-7064 (2000)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 3 figures

Scientific paper

10.1103/PhysRevE.62.7059

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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