Size distribution of communities at different scales
Fast unfolding of communities in large networks
Vincent D. Blondel, Jean-Loup Guillaume, Renaud Lambiotte, Etienne Lefebvre
J. Stat. Mech. (october 2008) P10008
We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks
Computing communities in large networks using random walks
Pascal Pons and Matthieu Latapy
Journal of Graph Algorithms and Applications (JGAA) vol. 10, no. 2, pages 191-218, 2006. Extended abstract published in LNCS, proceedings of the 20-th International Symposium on Computer and Information Sciences ISCIS’05, 2005, Istambul, Turquie
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn) and space O(n) in the worst case, and in time O(n log n) and space O(n) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.