k-Clique Percolation and Clustering [chapter]

Gergely Palla, Dániel Ábel, Illés J. Farkas, Péter Pollner, Imre Derényi, Tamás Vicsek
2008 Bolyai Society Mathematical Studies  
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 kclique 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
more » ... n-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.
doi:10.1007/978-3-540-69395-6_9 fatcat:sesxqpbbknao7pnljyq45vlphy