Exact solution of bond percolation on small arbitrary graphs

Details Exact solution of bond percolation on small arbitrary graphs Exact solution of bond percolation on small arbitrary graphs

2012-01-20

arxiv.org/abs/1201.4369v1

Physics

Condensed Matter

Statistical Mechanics

5 pages and 3 figures

Scientific paper

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.

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