English

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

Statistical Mechanics 2009-10-31 v1 Disordered Systems and Neural Networks q-bio

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.

Keywords

Cite

@article{arxiv.cond-mat/0001393,
  title  = {Exact solution of site and bond percolation on small-world networks},
  author = {Cristopher Moore and M. E. J. Newman},
  journal= {arXiv preprint arXiv:cond-mat/0001393},
  year   = {2009}
}

Comments

13 pages, 3 figures