Community detection by fuzzy clustering

How to measure the similarity between nodes is of great importance for fuzzy clustering when we use the approach to uncover communities in complex networks. In this paper, we first measure the similarity between nodes in a network based on edge centralities and model the network as a fuzzy relation. Then, two fuzzy transitive rules (Rule I and Rule II) are applied on the relation respectively, by which the similarity information can be transferred from one node to another in the network until the relation reaches a stable state. By choosing different thresholds, our method finally can partition the network into several non-overlapping subgroups. We compare our method with some state of the art methods on the LFR benchmark and real-world networks. We find that our method based on Rule I can correctly identify communities when the similarity between nodes of same groups is greater than that of different groups, while it is just opposite to Rule II. Our method achieves better results than the state of the art methods when the pre-planted communities of the random networks are vaguer.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  John Scott.  What is social network analysis , 2010 .

[3]  Boleslaw K. Szymanski,et al.  Overlapping community detection in networks: The state-of-the-art and comparative study , 2011, CSUR.

[4]  J. Sambles,et al.  Slow waves caused by cuts perpendicular to a single subwavelength slit in metal , 2007 .

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

[6]  Y. Kivshar,et al.  Wide-band negative permeability of nonlinear metamaterials , 2012, Scientific Reports.

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

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

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

[10]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[11]  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.

[12]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[13]  James P. Bagrow,et al.  Communities and bottlenecks: trees and treelike networks have high modularity. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[16]  Yang Yang,et al.  Maximizing modularity intensity for community partition and evolution , 2013, Inf. Sci..

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

[18]  Boris G. Mirkin,et al.  Additive spectral method for fuzzy cluster analysis of similarity data including community structure and affinity matrices , 2012, Inf. Sci..

[19]  Peng Gang Sun,et al.  Weighting links based on edge centrality for community detection , 2014 .

[20]  Massimo Marchiori,et al.  Vulnerability and protection of infrastructure networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Lin Gao,et al.  Identification of overlapping and non-overlapping community structure by fuzzy clustering in complex networks , 2011, Inf. Sci..

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

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

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

[25]  Pasquale De Meo,et al.  Enhancing community detection using a network weighting strategy , 2013, Inf. Sci..

[26]  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.

[27]  Luonan Chen,et al.  Quantitative function for community detection. , 2008 .

[28]  Martin Rosvall,et al.  Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems , 2010, PloS one.

[29]  Dong Zhou,et al.  Translation techniques in cross-language information retrieval , 2012, CSUR.

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

[31]  Martin Rosvall,et al.  An information-theoretic framework for resolving community structure in complex networks , 2007, Proceedings of the National Academy of Sciences.

[32]  Yang Yang,et al.  Methods to find community based on edge centrality , 2013 .

[33]  Mark S. Granovetter.  Economic Action and Social Structure: The Problem of Embeddedness , 1985, American Journal of Sociology.

[34]  Hocine Cherifi,et al.  Comparative evaluation of community detection algorithms: a topological approach , 2012, ArXiv.

[35]  Santo Fortunato,et al.  Consensus clustering in complex networks , 2012, Scientific Reports.

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

[37]  Santo Fortunato,et al.  Finding Statistically Significant Communities in Networks , 2010, PloS one.

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

[39]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[40]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

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

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