Abstract
Automatic detection of relevant groups of nodes in large real-world graphs, i.e. community detection, has applications in many fields and has received a lot of attention in the last twenty years. The most popular method designed to find overlapping communities (where a node can belong to several communities) is perhaps the clique percolation method (cpm). This method formalizes the notion of community as a maximal union of k-cliques that can be reached from each other through a series of adjacent k-cliques, where two cliques are adjacent if and only if they overlap on \(k-1\) nodes. Despite much effort cpm has not been scalable to large graphs for medium values of k.
Recent work has shown that it is possible to efficiently list all k-cliques in very large real-world graphs for medium values of k. We build on top of this work and scale up cpm. In cases where this first algorithm faces memory limitations, we propose another algorithm, cpmz, that provides a solution close to the exact one, using more time but less memory.
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Notes
- 1.
Notice that if a node does not belong to at least one k-clique, it doesn’t belong to any community.
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Acknowledgements
This work was partly supported by projects ANER ARTICO (Bourgogne-Franche-Comté region), ANR (French National Agency of Research) Limass project (under grant ANR-19-CE23-0010), ANR FiT LabCom and ANR COREGRAPHIE project (grant ANR-20-CE23-0002). We would like to greatly thank Lionel Tabourier for insightful discussions, useful comments and suggestions, and Fabrice Lecuyer for his careful proofreading.
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Baudin, A., Danisch, M., Kirgizov, S., Magnien, C., Ghanem, M. (2022). Clique Percolation Method: Memory Efficient Almost Exact Communities. In: Li, B., et al. Advanced Data Mining and Applications. ADMA 2022. Lecture Notes in Computer Science(), vol 13088. Springer, Cham. https://doi.org/10.1007/978-3-030-95408-6_9
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