Fast unfolding of communities in large networks

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 methods 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 million customers and by analysing 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.

[1]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[2]  J. M. Oshorn Proc. Nat. Acad. Sei , 1978 .

[3]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[4]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[5]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Fang Wu,et al.  Finding communities in linear time: a physics approach , 2003, ArXiv.

[7]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M. Newman Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  R. Guimerà,et al.  Modularity from fluctuations in random graphs and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Stefan Bornholdt,et al.  Detecting fuzzy community structures in complex networks with a Potts model. , 2004, Physical review letters.

[14]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Matthieu Latapy,et al.  Computing Communities in Large Networks Using Random Walks , 2004, J. Graph Algorithms Appl..

[16]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[17]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[18]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[19]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[22]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[23]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[24]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  R. Lambiotte,et al.  Majority model on a network with communities. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Sergio Gómez,et al.  Size reduction of complex networks preserving modularity , 2007, ArXiv.

[27]  Roger Guimerà,et al.  Extracting the hierarchical organization of complex systems , 2007, Proceedings of the National Academy of Sciences.

[28]  A. Barabasi,et al.  Quantifying social group evolution , 2007, Nature.

[29]  Etienne Huens,et al.  Geographical dispersal of mobile communication networks , 2008, 0802.2178.

[30]  Alex Arenas,et al.  Analysis of the structure of complex networks at different resolution levels , 2007, physics/0703218.

[31]  V. Blondel,et al.  Ju l 2 00 8 Fast unfolding of communities in large networks , 2008 .

[32]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.