Finding and evaluating community structure in networks.

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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

[2]  J. Anthonisse.  The rush in a directed graph , 1971 .

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

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

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

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  M. Garey.  Johnson: computers and intractability: a guide to the theory of np- completeness (freeman , 1979 .

[8]  B. Efron.  Computers and the Theory of Statistics: Thinking the Unthinkable , 1979 .

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

[10]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

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

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

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

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

[15]  Thorsten von Eicken,et al.  技術解説 IEEE Computer , 1999 .

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

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

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

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

[20]  김삼묘,et al.  “Bioinformatics” 특집을 내면서 , 2000 .

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

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

[23]  V. Latora,et al.  Harmony in the Small-World , 2000, cond-mat/0008357.

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

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

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

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

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

[29]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[30]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

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

[32]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[34]  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.

[35]  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.

[36]  P. Viot,et al.  Evidence for "fragile" glass-forming behavior in the relaxation of Coulomb frustrated three-dimensional systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[38]  Dennis M. Wilkinson,et al.  Finding Communities of Related Genes , 2002, cond-mat/0210147.

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

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

[41]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[43]  M. Newman,et al.  Origin of degree correlations in the Internet and other networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[46]  Petter Holme,et al.  Subnetwork hierarchies of biochemical pathways , 2002, Bioinform..

[47]  Lada A. Adamic,et al.  Friends and neighbors on the Web , 2003, Soc. Networks.

[48]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

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

[51]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[52]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .