The critical point of k-clique percolation in the Erdos-Rényi graph

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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-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).

Original languageEnglish
Pages (from-to)219-227
Number of pages9
JournalJournal of Statistical Physics
Issue number1-2
Publication statusPublished - Jul 1 2007



  • Community
  • Network
  • Percolation
  • Random graph

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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