Exact solution of site and bond percolation on small-world networks
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 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.
- Publication:
-
Physical Review E
- Pub Date:
- November 2000
- DOI:
- 10.1103/PhysRevE.62.7059
- arXiv:
- arXiv:cond-mat/0001393
- Bibcode:
- 2000PhRvE..62.7059M
- Keywords:
-
- 87.23.Ge;
- 84.35.+i;
- 05.70.Jk;
- 64.60.Ak;
- Dynamics of social systems;
- Neural networks;
- Critical point phenomena;
- Renormalization-group fractal and percolation studies of phase transitions;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Quantitative Biology
- E-Print:
- 13 pages, 3 figures