Exact solution of percolation on random graphs with arbitrary degree distributions
Abstract
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to deletion of network nodes. Such deletions include, for example, the failure of internet routers or power transmission lines. Percolation on random graphs provides a simple model of this process, but has in the past been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of properties of interest for site, bond, and joint site/bond percolation, including the position of the percolation transition, average cluster size, and size of the giant component. We discuss the application of our theory to the understanding of network resilience.Keywords
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