Community detection based on network communicability.

We propose a new method for detecting communities based on the concept of communicability between nodes in a complex network. This method, designated as N-ComBa K-means, uses a normalized version of the adjacency matrix to build the communicability matrix and then applies K-means clustering to find the communities in a graph. We analyze how this method performs for some pathological cases found in the analysis of the detection limit of communities and propose some possible solutions on the basis of the analysis of the ratio of local to global densities in graphs. We use four different quality criteria for detecting the best clustering and compare the new approach with the Girvan-Newman algorithm for the analysis of two "classical" networks: karate club and bottlenose dolphins. Finally, we analyze the more challenging case of homogeneous networks with community structure, for which the Girvan-Newman completely fails in detecting any clustering. The N-ComBa K-means approach performs very well in these situations and we applied it to detect the community structure in an international trade network of miscellaneous manufactures of metal having these characteristics. Some final remarks about the general philosophy of community detection are also discussed.

[1]  Santosh S. Vempala,et al.  On clusterings: Good, bad and spectral , 2004, JACM.

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

[3]  Ernesto Estrada,et al.  Communicability graph and community structures in complex networks , 2009, Appl. Math. Comput..

[4]  Natasa Przulj,et al.  Biological network comparison using graphlet degree distribution , 2007, Bioinform..

[5]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

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

[7]  Ulrik Brandes,et al.  Engineering graph clustering: Models and experimental evaluation , 2008, JEAL.

[8]  Martin G. Everett,et al.  A Graph-theoretic perspective on centrality , 2006, Soc. Networks.

[9]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

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

[11]  Ernesto Estrada.  Generalized walks-based centrality measures for complex biological networks. , 2010, Journal of theoretical biology.

[12]  M. Benzi,et al.  Quadrature rule-based bounds for functions of adjacency matrices , 2010 .

[13]  Natali Gulbahce,et al.  The art of community detection , 2008, BioEssays : news and reviews in molecular, cellular and developmental biology.

[14]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[15]  Damir Vukicevic,et al.  A note on the Estrada-Hatano communicability algorithm for detecting community structure in complex networks , 2010, Appl. Math. Comput..

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

[17]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[18]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[19]  Desmond J. Higham,et al.  Network Science - Complexity in Nature and Technology , 2010, Network Science.

[20]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[21]  Jian Liu,et al.  Comparative Analysis for k-Means Algorithms in Network Community Detection , 2010, ISICA.

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

[23]  Bethany S. Dohleman.  Exploratory social network analysis with Pajek , 2006 .

[24]  Andrew B. Kahng,et al.  Spectral Partitioning with Multiple Eigenvectors , 1999, Discret. Appl. Math..

[25]  D. Higham,et al.  A weighted communicability measure applied to complex brain networks , 2009, Journal of The Royal Society Interface.

[26]  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.

[27]  Donald W. Bouldin,et al.  A Cluster Separation Measure , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Ernesto Estrada,et al.  Spectral scaling and good expansion properties in complex networks , 2006, Europhysics Letters (EPL).

[29]  S. Dongen.  Performance criteria for graph clustering and Markov cluster experiments , 2000 .

[30]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

[31]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

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

[33]  Francisco Azuaje,et al.  Cluster validation techniques for genome expression data , 2003, Signal Process..

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

[35]  Ernesto Estrada,et al.  Communicability in complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[37]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[38]  Amnon Shashua,et al.  A unifying approach to hard and probabilistic clustering , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[39]  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.

[40]  Desmond J. Higham,et al.  Network Properties Revealed through Matrix Functions , 2010, SIAM Rev..

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