Characterizing and Extracting Multiplex Patterns in Complex Networks

Complex network theory provides a means for modeling and analyzing complex systems that consist of multiple and interdependent components. Among the studies on complex networks, structural analysis is of fundamental importance as it presents a natural route to understanding the dynamics, as well as to synthesizing or optimizing the functions, of networks. A wide spectrum of structural patterns of networks has been reported in the past decade, such as communities, multipartites, bipartite, hubs, authorities, outliers, and bow ties, among others. In this paper, we are interested in tackling the challenging task of characterizing and extracting multiplex patterns (multiple patterns as mentioned previously coexisting in the same networks in a complicated manner), which so far has not been explicitly and adequately addressed in the literature. Our work shows that such multiplex patterns can be well characterized as well as effectively extracted by means of a granular stochastic blockmodel, together with a set of related algorithms proposed here based on some machine learning and statistical inference ideas. These models and algorithms enable us to further explore complex networks from a novel perspective.

[1]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[2]  Chris H Wiggins,et al.  Bayesian approach to network modularity. , 2007, Physical review letters.

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

[4]  Roger Guimerà,et al.  Extracting the hierarchical organization of complex systems , 2007, Proceedings of the National Academy of Sciences.

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

[6]  Christos Faloutsos,et al.  Graph mining: Laws, generators, and algorithms , 2006, CSUR.

[7]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

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

[9]  Yihong Gong,et al.  Detecting communities and their evolutions in dynamic social networks—a Bayesian approach , 2011, Machine Learning.

[10]  David A. Smith,et al.  Structure and Dynamics of the Global Economy: Network Analysis of International Trade 1965–1980 , 1992 .

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

[12]  Jean-Loup Guillaume,et al.  Bipartite structure of all complex networks , 2004, Inf. Process. Lett..

[13]  K. Reitz,et al.  Graph and Semigroup Homomorphisms on Networks of Relations , 1983 .

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

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

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

[17]  Kathryn B. Laskey,et al.  Stochastic blockmodels: First steps , 1983 .

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

[19]  P. Holland,et al.  Local Structure in Social Networks , 1976 .

[20]  S. Fienberg,et al.  Categorical Data Analysis of Single Sociometric Relations , 1981 .

[21]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

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

[23]  M. Newman,et al.  Hierarchical structure and the prediction of missing links in networks , 2008, Nature.

[24]  The web is a bow tie , 2000, Nature.

[25]  Petter Holme,et al.  Network bipartivity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  An-Ping Zeng,et al.  The Connectivity Structure, Giant Strong Component and Centrality of Metabolic Networks , 2003, Bioinform..

[27]  R. Lambiotte,et al.  Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks , 2008, IEEE Transactions on Network Science and Engineering.

[28]  E A Leicht,et al.  Mixture models and exploratory analysis in networks , 2006, Proceedings of the National Academy of Sciences.

[29]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[30]  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.

[31]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[32]  Edoardo M. Airoldi,et al.  Mixed Membership Stochastic Blockmodels , 2007, NIPS.

[33]  Arthur Brady,et al.  Fault Tolerance in Protein Interaction Networks: Stable Bipartite Subgraphs and Redundant Pathways , 2009, PloS one.

[34]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

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

[37]  H. White,et al.  STRUCTURAL EQUIVALENCE OF INDIVIDUALS IN SOCIAL NETWORKS , 1977 .

[38]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.