Detection of structurally homogeneous subsets in graphs

The analysis of complex networks is a rapidly growing topic with many applications in different domains. The analysis of large graphs is often made via unsupervised classification of vertices of the graph. Community detection is the main way to divide a large graph into smaller ones that can be studied separately. However another definition of a cluster is possible, which is based on the structural distance between vertices. This definition includes the case of community clusters but is more general in the sense that two vertices may be in the same group even if they are not connected. Methods for detecting communities in undirected graphs have been recently reviewed by Fortunato. In this paper we expand Fortunato’s work and make a review of methods and algorithms for detecting essentially structurally homogeneous subsets of vertices in binary or weighted and directed and undirected graphs.

[1]  Jean-Jacques Daudin,et al.  A review of statistical models for clustering networks with an application to a PPI network , 2011 .

[2]  Samuel Leinhardt,et al.  Roles and Positions: A Critique and Extension of the Blockmodeling Approach , 1983 .

[3]  Bin Yu,et al.  Spectral clustering and the high-dimensional stochastic blockmodel , 2010, 1007.1684.

[4]  Daniel B. Stouffer,et al.  Origin of compartmentalization in food webs. , 2010, Ecology.

[5]  Kenneth G. Manton,et al.  Statistical applications using fuzzy sets , 1994 .

[6]  Jean-Jacques Daudin,et al.  Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network , 2010, Biometrics.

[7]  Jacques van Helden,et al.  Evaluation of clustering algorithms for protein-protein interaction networks , 2006, BMC Bioinformatics.

[8]  Cristopher Moore,et al.  Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  C. Matias,et al.  New consistent and asymptotically normal parameter estimates for random‐graph mixture models , 2012 .

[10]  Franck Picard,et al.  A mixture model for random graphs , 2008, Stat. Comput..

[11]  A. Hoffman,et al.  Lower bounds for the partitioning of graphs , 1973 .

[12]  P. Bickel,et al.  A nonparametric view of network models and Newman–Girvan and other modularities , 2009, Proceedings of the National Academy of Sciences.

[13]  Phipps Arabie,et al.  Constructing blockmodels: How and why , 1978 .

[14]  A. Raftery,et al.  Model‐based clustering for social networks , 2007 .

[15]  H. Hirschfeld.  A Connection between Correlation and Contingency , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  P. Latouche,et al.  Overlapping stochastic block models with application to the French political blogosphere , 2009, 0910.2098.

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

[18]  F. Cailliez.  Analyse des données , 1984 .

[19]  Christophe Ambroise,et al.  Overlapping Stochastic Block Models , 2009 .

[20]  Gilbert Saporta,et al.  L'analyse des données , 1981 .

[21]  St'ephane Robin,et al.  Uncovering latent structure in valued graphs: A variational approach , 2010, 1011.1813.

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

[23]  Samuel Kaski,et al.  Inferring Vertex Properties from Topology in Large Networks , 2007, MLG.

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

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

[26]  Franck Picard,et al.  Deciphering the connectivity structure of biological networks using MixNet , 2009, BMC Bioinformatics.

[27]  Chris Wiggins,et al.  An Information-Theoretic Derivation of Min-Cut-Based Clustering , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  S. vanDongen.  Graph Clustering by Flow Simulation , 2000 .

[29]  David J. Marchette,et al.  Predicting unobserved links in incompletely observed networks , 2008, Comput. Stat. Data Anal..

[30]  Janne Sinkkonen,et al.  Component models for large networks , 2008, 0803.1628.

[31]  Nickolay T. Trendafilov,et al.  GIPSCAL revisited. A projected gradient approach , 2002, Stat. Comput..

[32]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure , 1997 .

[33]  S. Boorman,et al.  Social Structure from Multiple Networks. II. Role Structures , 1976, American Journal of Sociology.

[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]  Alain Celisse,et al.  Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model , 2011, 1105.3288.

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

[37]  S. Boorman,et al.  Social structure from multiple networks: I , 1976 .

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

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

[40]  Edoardo M. Airoldi,et al.  Stochastic blockmodels with growing number of classes , 2010, Biometrika.

[41]  E. Erosheva.  Comparing Latent Structures of the Grade of Membership, Rasch, and Latent Class Models , 2005 .

[42]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[43]  Matthieu Latapy,et al.  Computing Communities in Large Networks Using Random Walks , 2004, J. Graph Algorithms Appl..

[44]  Ronald S. Burt,et al.  Cohesion Versus Structural Equivalence as a Basis for Network Subgroups , 1978 .

[45]  M. Volle.  Analyse des données , 1978 .

[46]  S. Boorman,et al.  Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions , 1976, American Journal of Sociology.

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

[48]  Y. Takane,et al.  A generalization of Takane's algorithm for dedicom , 1990 .

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

[50]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .