Аннотация
Recent work on the internet, social networks, and the power grid has
addressed the resilience of these networks to either random or targeted
deletion of network nodes. Such deletions include, for example, the failure of
internet routers or power transmission lines. Percolation models on random
graphs provide a simple representation of this process, but have typically 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 cases, including site percolation, bond percolation, and models in
which occupation probabilities depend on vertex degree. We discuss the
application of our theory to the understanding of network resilience.
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