Exact solution of bond percolation on small arbitrary graphs
Statistical Mechanics
2012-04-30 v2 Social and Information Networks
Physics and Society
Abstract
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.
Cite
@article{arxiv.1201.4369,
title = {Exact solution of bond percolation on small arbitrary graphs},
author = {Antoine Allard and Laurent Hébert-Dufresne and Pierre-André Noël and Vincent Marceau and Louis J. Dubé},
journal= {arXiv preprint arXiv:1201.4369},
year = {2012}
}
Comments
5 pages and 3 figures