Abstract
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdős–Rényi graph. When the probability p of two nodes being connected is above a certain threshold p c (k), the complete subgraphs of size k (the k-cliques) are organized into a giant cluster. By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism. From the divergence of this average size we then derive an analytic expression for the critical linking probability p c (k).
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Palla, G., Derényi, I. & Vicsek, T. The Critical Point of k-Clique Percolation in the Erdős–Rényi Graph. J Stat Phys 128, 219–227 (2007). https://doi.org/10.1007/s10955-006-9184-x
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DOI: https://doi.org/10.1007/s10955-006-9184-x