Exact Computation of Percolation Cluster Sizes in Finite Networks

Abstract

[eng] Bond percolation in real networks is a well known problem of statistical physics with many applications from epidemic spreading to network robustness analysis. In particular, we focus on the design of a new algorithm for the computation of exact values of the percolation estimates. Due to the scaling of the possible number of configurations of the percolation process with the network size, there has been a huge emphasis on the computation of these estimates using approximations or Monte-Carlo methods instead of the search of an exact solution. We have used equivalence relations in the nodes set called Cluster Constellations (CC) in order to reduce the complexity in the description of the percolation configurations. An algorithm which uses these equivalence relations has been implemented in order to obtain exact percolation quantities. For certain networks of interest including the famous Karate Club Network we are able to compute exact expected cluster sizes for the first time.