Closed walks for community detection

In this paper, we propose a novel measure that integrates both the concept of closed walks and clustering coefficients to replace the edge betweenness in the well-known divisive hierarchical clustering algorithm, the Girvan and Newman method (GN). The edges with the lowest value are removed iteratively until the network is degenerated into isolated nodes. The experimental results on computer generated networks and real-world networks showed that our method makes a better tradeoff of accuracy and runtime. Based on the analysis of the results, we observe that the nontrivial closed walks of order three and four can be considered as the basic elements in constructing community structures. Meanwhile, we discover that those nontrivial closed walks outperform trivial closed walks in the task of analyzing the structure of networks. The double peak structure problem is mentioned in the last part of the article. We find that our proposed method is a novel way to solve the double peak structure problem. Our work can provide us with a new perspective for understanding community structure in complex networks.

[1]  Neo D. Martinez,et al.  Food-web structure and network theory: The role of connectance and size , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[2]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Susan K. Walker.  Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives , 2011 .

[4]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[5]  Mark E. J. Newman,et al.  Random graphs containing arbitrary distributions of subgraphs , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[8]  Krithi Ramamritham,et al.  Real Time Discovery of Dense Clusters in Highly Dynamic Graphs: Identifying Real World Events in Highly Dynamic Environments , 2012, Proc. VLDB Endow..

[9]  Delbert Dueck,et al.  Clustering by Passing Messages Between Data Points , 2007, Science.

[10]  Massimo Marchiori,et al.  Method to find community structures based on information centrality. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  V. Latora,et al.  A measure of centrality based on network efficiency , 2004, cond-mat/0402050.

[12]  Shuigeng Zhou,et al.  Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices , 2007 .

[13]  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.

[14]  S. Redner.  How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[15]  Sune Lehmann,et al.  Link communities reveal multiscale complexity in networks , 2009, Nature.

[16]  Jacobs,et al.  Generic rigidity percolation in two dimensions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  P. Arabie,et al.  An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling , 1975 .

[18]  B. Grenfell,et al.  Mean-field-type equations for spread of epidemics: the ‘small world’ model , 1999 .

[19]  Yicheng Zhang,et al.  Identifying influential nodes in complex networks , 2012 .

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

[22]  Min Wu,et al.  A core-attachment based method to detect protein complexes in PPI networks , 2009, BMC Bioinformatics.

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

[24]  I. N. A. C. I. J. H. Fowler.  Book Review: Connected: The surprising power of our social networks and how they shape our lives. , 2009 .

[25]  Javier Béjar,et al.  Clustering algorithm for determining community structure in large networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Roger Guimerà,et al.  Robust patterns in food web structure. , 2001, Physical review letters.

[27]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Massimo Marchiori,et al.  Economic small-world behavior in weighted networks , 2003 .

[29]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[30]  W. Kowalchuck,et al.  On self similarity , 1980 .

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

[32]  Haijun Zhou.  Distance, dissimilarity index, and network community structure. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[34]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality and clustering in complex hyper-networks , 2006 .

[35]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  R. Sharan,et al.  Network-based prediction of protein function , 2007, Molecular systems biology.

[37]  Lada A. Adamic,et al.  The political blogosphere and the 2004 U.S. election: divided they blog , 2005, LinkKDD '05.

[38]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[39]  David Lusseau,et al.  The emergent properties of a dolphin social network , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

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

[42]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

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

[44]  M. L. Sachtjen,et al.  Disturbances in a power transmission system , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[45]  D. Fell,et al.  The small world inside large metabolic networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[46]  Luonan Chen,et al.  Network‐Based Prediction of Protein Function , 2009 .

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

[48]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

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

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

[51]  S. Borgatti,et al.  The centrality of groups and classes , 1999 .