Community Structures of Networks

Abstract.We present an approach to studying the community structures of networks by using linear programming (LP). Starting with a network in terms of (a) a collection of nodes and (b) a collection of edges connecting some of these nodes, we use a new LP-based method for simultaneously (i) finding, at minimal cost, a second edge set by deleting existing and inserting additional edges so that the network becomes a disjoint union of cliques and (ii) appropriately calibrating the costs for doing so. We provide examples that suggest that, in practice, this approach provides a surprisingly good strategy for detecting community structures in given networks.

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

[2]  A. Clauset.  Finding local community structure in networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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

[6]  Alain Guénoche,et al.  Maximum Transfer Distance Between Partitions , 2006, J. Classif..

[7]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

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

[9]  R. Ulanowicz,et al.  The Seasonal Dynamics of The Chesapeake Bay Ecosystem , 1989 .

[10]  Karl-Heinz Borgwardt,et al.  The Average number of pivot steps required by the Simplex-Method is polynomial , 1982, Z. Oper. Research.

[11]  Karl Heinz Borgwardt,et al.  Some Distribution-Independent Results About the Asymptotic Order of the Average Number of Pivot Steps of the Simplex Method , 1982, Math. Oper. Res..

[12]  Martin Grötschel,et al.  Facets of the clique partitioning polytope , 1990, Math. Program..

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

[14]  S.,et al.  An Efficient Heuristic Procedure for Partitioning Graphs , 2022 .

[15]  John Scott.  Social Network Analysis , 1988 .

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

[17]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[18]  Robert E. Ulanowicz,et al.  Quantitative methods for ecological network analysi , 2004, Comput. Biol. Chem..

[19]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

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

[21]  S. Wasserman,et al.  Social Network Analysis: Computer Programs , 1994 .

[22]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[23]  John M. Carroll.  Proceedings of the fourth international conference on Communities and technologies , 2009 .

[24]  H. William Hunt,et al.  Resource compartmentation and the stability of real ecosystems , 1988, Nature.

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

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

[27]  L. Hood,et al.  A Genomic Regulatory Network for Development , 2002, Science.

[28]  M. A. Muñoz,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Detecting network communities: a new systematic and efficient algorithm , 2004 .

[29]  Jon Kleinberg,et al.  The Structure of the Web , 2001, Science.

[30]  C. Lee Giles,et al.  Self-Organization and Identification of Web Communities , 2002, Computer.

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

[32]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[33]  Bernardo A. Huberman,et al.  Email as spectroscopy: automated discovery of community structure within organizations , 2003 .

[34]  Carson C. Chow,et al.  Small Worlds , 2000 .

[35]  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.

[36]  Yoshiko Wakabayashi,et al.  A cutting plane algorithm for a clustering problem , 1989, Math. Program..

[37]  S. Grant,et al.  The proteomes of neurotransmitter receptor complexes form modular networks with distributed functionality underlying plasticity and behaviour , 2006, Molecular systems biology.

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

[39]  Neo D. Martinez,et al.  Simple rules yield complex food webs , 2000, Nature.

[40]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[41]  Steve Smale,et al.  The Problem of the Average Speed of the Simplex Method , 1982, ISMP.

[42]  Erik M Bollt,et al.  Local method for detecting communities. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  D. Mason,et al.  Compartments revealed in food-web structure , 2003, Nature.

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

[45]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[48]  Bernardo A. Huberman,et al.  E-Mail as Spectroscopy: Automated Discovery of Community Structure within Organizations , 2005, Inf. Soc..

[49]  D. Eisenberg,et al.  Protein interaction databases. , 2001, Current opinion in biotechnology.

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

[51]  S. McNaughton,et al.  Stability and diversity of ecological communities , 1978, Nature.