Phase transition model for community detection

Motivated by social and biological interactions, a novel type of phase transition model is provided in order to investigate the emergence of the clustering phenomenon in networks. The model has two types of interactions: one is attractive and the other is repulsive. In each iteration, the phase of a node (or an agent) moves toward the average phase of its neighbors and moves away from the average phase of its non-neighbors. The velocities of the two types of phase transition are controlled by two parameters, respectively. It is found that the phase transition phenomenon is closely related to the topological structure of the underlying network, and thus can be applied to identify its communities and overlapping groups. By giving each node of the network a randomly generated initial phase and updating these phases by the phase transition model until they reach stability, one or two communities will be detected according to the nodes’ stable phases, confusable nodes are moved into a set named Of. By removing the detected communities and the nodes in Of, another one or two communities will be detected by an iteration of the algorithm, …. In this way, all communities and the overlapping nodes are detected. Simulations on both real-world networks and the LFR benchmark graphs have verified the efficiency of the proposed scheme.

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

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

[3]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[4]  Yong Zhang,et al.  Fuzzy analysis of community detection in complex networks , 2010 .

[5]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[6]  Jian Liu,et al.  Detecting community structure in complex networks using simulated annealing with k-means algorithms , 2010 .

[7]  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.

[8]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

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

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

[11]  I Leyva,et al.  Dynamics of overlapping structures in modular networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[13]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[16]  M. Newman.  Coauthorship networks and patterns of scientific collaboration , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Huawei Shen,et al.  Quantifying and identifying the overlapping community structure in networks , 2009, 0905.2666.

[18]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[19]  Jianzhi Zhang,et al.  In Search of the Biological Significance of Modular Structures in Protein Networks , 2007, PLoS Comput. Biol..

[20]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[21]  Mark E. J. Newman,et al.  An efficient and principled method for detecting communities in networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Zhipeng Lü,et al.  Iterated tabu search for identifying community structure in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Alexandre Arenas,et al.  Structural and functional networks in complex systems with delay , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Tao Zhou,et al.  Phase synchronization on scale-free networks with community structure , 2007 .

[26]  Licheng Jiao,et al.  Synchronization on overlapping community network , 2012 .

[27]  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.

[28]  J M Buldú,et al.  Synchronization interfaces and overlapping communities in complex networks. , 2008, Physical review letters.

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

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

[31]  Shihua Zhang,et al.  Identification of overlapping community structure in complex networks using fuzzy c-means clustering , 2007 .

[32]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[33]  S. Borgatti,et al.  Analyzing Clique Overlap , 2009 .

[34]  Yanay Ofran,et al.  Unveiling Protein Functions through the Dynamics of the Interaction Network , 2011, PloS one.

[35]  Shihua Zhang,et al.  Uncovering fuzzy community structure in complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Vladimir Gudkov,et al.  Community Detection in Complex Networks by Dynamical Simplex Evolution , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Jean-Cédric Chappelier,et al.  Finding instabilities in the community structure of complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[39]  Shuigeng Zhou,et al.  Evolutionary method for finding communities in bipartite networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[41]  Santo Fortunato,et al.  Limits of modularity maximization in community detection , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[43]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[44]  Michelle Girvan,et al.  Multiscale dynamics in communities of phase oscillators. , 2012, Chaos.

[45]  Ernesto Estrada,et al.  Community detection based on network communicability. , 2011, Chaos.

[46]  Xueqi Cheng,et al.  Spectral methods for the detection of network community structure: a comparative analysis , 2010, ArXiv.

[47]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

[48]  Huawei Shen,et al.  Covariance, correlation matrix, and the multiscale community structure of networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Jari Saramäki,et al.  Limited resolution and multiresolution methods in complex network community detection , 2007, SPIE International Symposium on Fluctuations and Noise.

[50]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[51]  E Oh,et al.  Modular synchronization in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Yamir Moreno,et al.  Fitness for synchronization of network motifs , 2004, cond-mat/0404054.

[53]  Xue-Qi Cheng,et al.  Uncovering the community structure associated with the diffusion dynamics on networks , 2009, 0911.2308.

[54]  Maoguo Gong,et al.  Overlapping community detection via network dynamics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  T. Nepusz,et al.  Fuzzy communities and the concept of bridgeness in complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.