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Clique percolation in random networks.

Imre Derényi1, Gergely Palla, Tamás Vicsek

  • 1Department of Biological Physics, Eötvös University, Pázmány P. stny. 1A, H-1117 Budapest, Hungary.

Physical Review Letters
|May 21, 2005
PubMed
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We introduce k-clique percolation in random graphs to study large-scale community structures. The study reveals a percolation transition for k-cliques, crucial for identifying overlapping communities in networks.

Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Understanding community structures in large networks is a significant challenge.
  • Percolation theory provides a framework for studying connectivity transitions in random systems.

Purpose of the Study:

  • To introduce and investigate k-clique percolation in random graphs.
  • To analytically and numerically study the large-scale organization of complete subgraphs (k-cliques).
  • To explore the application of clique percolation for identifying overlapping communities.

Main Methods:

  • Introduction of k-clique percolation framework.
  • Analytical investigation of k-clique percolation in Erdos-Rényi graphs.
  • Numerical simulations to study the scaling of the giant component.

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Main Results:

  • Derivation of the percolation transition threshold for k-cliques: p(c)(k) = [(k - 1)N](-1/(k - 1)).
  • Identification of a nontrivial scaling of the giant component with N at the transition point, dependent on k.
  • Demonstration of clique percolation as an effective method for community detection.

Conclusions:

  • K-clique percolation offers a novel approach to understanding network organization.
  • The identified percolation transition is key to detecting overlapping communities in complex networks.
  • This method holds promise for analyzing large, real-world network data.