Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 128, Issue 1-2, Pages 219-227Publisher
SPRINGER
DOI: 10.1007/s10955-006-9184-x
Keywords
random graph; network; percolation; community
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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 Erdos-Renyi 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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