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k-Clique Percolation and Clustering

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Handbook of Large-Scale Random Networks

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 18))

Abstract

We summarise recent results connected to the concept of k-clique percolation. This approach can be considered as a generalisation of edge percolation with a great potential as a community finding method in real-world graphs. We present a detailed study of the critical point for the appearance of a giant k-clique percolation cluster in the Erdős-Rényi-graph. The observed transition is continuous and at the transition point the scaling of the giant component with the number of vertices is highly non-trivial. The concept is extended to weighted and directed graphs as well. Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.

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Authors and Affiliations

  1. Statistical and Biological Physics Research Group of HAS, H-1117, Budapest, Pázmány Péter sétány 1/A, Hungary

    Gergely Palla, Illés J. Farkas, Péter Pollner & Tamás Vicsek

  2. Department of Biological Physics, Eötvös University, H-1117, Budapest, Pázmány Péter sétány 1/A, Hungary

    Dániel Ábel, Illés J. Farkas, Imre Derényi & Tamás Vicsek

Authors
  1. Gergely Palla
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  2. Dániel Ábel
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  3. Illés J. Farkas
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  4. Péter Pollner
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  5. Imre Derényi
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  6. Tamás Vicsek
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Editors and Affiliations

  1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, CB3 0WB, UK

    Béla Bollobás

  2. Dept. Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás  & Robert Kozma  & 

  3. Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Dezső Miklós

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Palla, G., Ábel, D., Farkas, I.J., Pollner, P., Derényi, I., Vicsek, T. (2008). k-Clique Percolation and Clustering. In: Bollobás, B., Kozma, R., Miklós, D. (eds) Handbook of Large-Scale Random Networks. Bolyai Society Mathematical Studies, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69395-6_9

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