2000/01/26 by Cristopher Moore, M. E. J. Newman · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Cluster size #Combinatorics #Complex Network Analysis Techniques #Computer science #Condensed matter physics #Critical exponent #Mathematics #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Transmissibility (structural dynamics) #cond-mat.dis-nn #cond-mat.stat-mech #q-bio
paper · pdf · doi:10.1103/physreve.62.7059
published as Phys. Rev. E 62, 7059-7064 (2000) · 13 pages, 3 figures
arxiv created 2000/01/26 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 critical exponents governing this transition, the mean and variance of the distribution of cluster sizes (disease outbreaks) below the transition, and the size of the giant component (epidemic) above the transition.