Community detection in networks: A user guide

Abstract Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other groups, though other patterns are possible. Identifying communities is an ill-defined problem. There are no universal protocols on the fundamental ingredients, like the definition of community itself, nor on other crucial issues, like the validation of algorithms and the comparison of their performances. This has generated a number of confusions and misconceptions, which undermine the progress in the field. We offer a guided tour through the main aspects of the problem. We also point out strengths and weaknesses of popular methods, and give directions to their use.

[1]  Raj Rao Nadakuditi,et al.  Graph spectra and the detectability of community structure in networks , 2012, Physical review letters.

[2]  Cristopher Moore,et al.  Community detection in networks with unequal groups , 2015, Physical review. E.

[3]  Philip S. Yu,et al.  Online Analysis of Community Evolution in Data Streams , 2005, SDM.

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

[5]  A. Arenas,et al.  Motif-based communities in complex networks , 2007, 0710.0059.

[6]  Reinhard Lipowsky,et al.  Network Brownian Motion: A New Method to Measure Vertex-Vertex Proximity and to Identify Communities and Subcommunities , 2004, International Conference on Computational Science.

[7]  J. Reichardt,et al.  Statistical mechanics of community detection. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  R. Baxter Exactly solved models in statistical mechanics , 1982 .

[9]  Martin Rosvall,et al.  Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems , 2010, PloS one.

[10]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[11]  Stephen B. Seidman,et al.  A graph‐theoretic generalization of the clique concept* , 1978 .

[12]  Jean-Charles Delvenne,et al.  Stability of graph communities across time scales , 2008, Proceedings of the National Academy of Sciences.

[13]  Carl T. Bergstrom,et al.  Mapping Change in Large Networks , 2008, PloS one.

[14]  Mark E. J. Newman,et al.  Spectral community detection in sparse networks , 2013, ArXiv.

[15]  Guido Caldarelli,et al.  Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science , 2007 .

[16]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

[17]  Eyke Hüllermeier,et al.  A Fuzzy Variant of the Rand Index for Comparing Clustering Structures , 2009, IFSA/EUSFLAT Conf..

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

[19]  Alex Arenas,et al.  Community structure identification , 2005 .

[20]  Jure Leskovec,et al.  Community-Affiliation Graph Model for Overlapping Network Community Detection , 2012, 2012 IEEE 12th International Conference on Data Mining.

[21]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

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

[23]  Mark D. Humphries,et al.  Modular Deconstruction Reveals the Dynamical and Physical Building Blocks of a Locomotion Motor Program , 2015, Neuron.

[24]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[25]  M. Barber Modularity and community detection in bipartite networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Mark D. Humphries,et al.  Finding communities in sparse networks , 2015, Scientific Reports.

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

[28]  R. Luce,et al.  Connectivity and generalized cliques in sociometric group structure , 1950, Psychometrika.

[29]  S. Dongen Graph clustering by flow simulation , 2000 .

[30]  Charu C. Aggarwal,et al.  Social Network Data Analytics , 2011 .

[31]  J. Friedman,et al.  THE NON-BACKTRACKING SPECTRUM OF THE UNIVERSAL COVER OF A GRAPH , 2007, 0712.0192.

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

[33]  Tiago P. Peixoto Model selection and hypothesis testing for large-scale network models with overlapping groups , 2014, ArXiv.

[34]  Richard M. Karp,et al.  Algorithms for graph partitioning on the planted partition model , 2001, Random Struct. Algorithms.

[35]  D. R. White,et al.  Structural cohesion and embeddedness: A hierarchical concept of social groups , 2003 .

[36]  Jure Leskovec,et al.  Community Detection in Networks with Node Attributes , 2013, 2013 IEEE 13th International Conference on Data Mining.

[37]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[38]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[39]  Santo Fortunato,et al.  Consensus clustering in complex networks , 2012, Scientific Reports.

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

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

[42]  Srinivasan Parthasarathy,et al.  Community Discovery in Social Networks: Applications, Methods and Emerging Trends , 2011, Social Network Data Analytics.

[43]  Christophe Ambroise,et al.  Fast online graph clustering via Erdös-Rényi mixture , 2008, Pattern Recognit..

[44]  L. Christophorou Science , 2018, Emerging Dynamics: Science, Energy, Society and Values.

[45]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[46]  Cristopher Moore,et al.  Scalable detection of statistically significant communities and hierarchies, using message passing for modularity , 2014, Proceedings of the National Academy of Sciences.

[47]  Mason A. Porter,et al.  Communities in Networks , 2009, ArXiv.

[48]  Jure Leskovec,et al.  Overlapping community detection at scale: a nonnegative matrix factorization approach , 2013, WSDM.

[49]  Jure Leskovec,et al.  Higher-order organization of complex networks , 2016, Science.

[50]  Camille Roth,et al.  Natural Scales in Geographical Patterns , 2017, Scientific Reports.

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

[52]  L. Collins,et al.  Omega: A General Formulation of the Rand Index of Cluster Recovery Suitable for Non-disjoint Solutions. , 1988, Multivariate behavioral research.

[53]  Srinivasan Parthasarathy,et al.  An event-based framework for characterizing the evolutionary behavior of interaction graphs , 2007, KDD '07.

[54]  HERBERT A. SIMON,et al.  The Architecture of Complexity , 1991 .

[55]  Isabelle Guyon,et al.  A Stability Based Method for Discovering Structure in Clustered Data , 2001, Pacific Symposium on Biocomputing.

[56]  Martin Rosvall,et al.  Comparing network covers using mutual information , 2012, ArXiv.

[57]  Andrea Lancichinetti,et al.  Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Boleslaw K. Szymanski,et al.  Towards Linear Time Overlapping Community Detection in Social Networks , 2012, PAKDD.

[59]  R. Guimerà,et al.  Modularity from fluctuations in random graphs and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  M. Meilă Comparing clusterings---an information based distance , 2007 .

[61]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[62]  Xiao Zhang,et al.  Identification of core-periphery structure in networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  Santo Fortunato,et al.  Eigenvector dynamics under perturbation of modular networks , 2016, Physical review. E.

[64]  Tiago P Peixoto,et al.  Parsimonious module inference in large networks. , 2012, Physical review letters.

[65]  Santo Fortunato,et al.  Network structure, metadata and the prediction of missing nodes , 2016, ArXiv.

[66]  Reuven Cohen,et al.  Complex Networks: Structure, Robustness and Function , 2010 .

[67]  Renaud Lambiotte,et al.  Uncovering space-independent communities in spatial networks , 2010, Proceedings of the National Academy of Sciences.

[68]  Niloy Ganguly,et al.  Metrics for Community Analysis: A Survey , 2016 .

[69]  Mason A. Porter,et al.  Comparing Community Structure to Characteristics in Online Collegiate Social Networks , 2008, SIAM Rev..

[70]  Malik Magdon-Ismail,et al.  Finding communities by clustering a graph into overlapping subgraphs , 2005, IADIS AC.

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

[72]  Charlotte M. Deane,et al.  The function of communities in protein interaction networks at multiple scales , 2009, BMC Systems Biology.

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

[74]  Jon Kleinberg,et al.  KDD '07: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining , 2007, KDD 2007.

[75]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

[76]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[77]  Mark A. Pitt,et al.  Advances in Minimum Description Length: Theory and Applications , 2005 .

[78]  Jianbin Huang,et al.  Towards Online Multiresolution Community Detection in Large-Scale Networks , 2011, PloS one.

[79]  Albert-Laszló Barabási,et al.  Bursts : the hidden patterns behind everything we do, from your e-mail to bloody crusades , 2011 .

[80]  Boris Goldengorin,et al.  Handbook of combinatorial optimization , 2013 .

[81]  Robert L. Brennan,et al.  MEASURING AGREEMENT WHEN TWO OBSERVERS CLASSIFY PEOPLE INTO CATEGORIES NOT DEFINED IN ADVANCE , 1974 .

[82]  Jasmine Novak,et al.  Geographic routing in social networks , 2005, Proc. Natl. Acad. Sci. USA.

[83]  Myra Spiliopoulou,et al.  Evolution in Social Networks: A Survey , 2011, Social Network Data Analytics.

[84]  D. Wilkin,et al.  Neuron , 2001, Brain Research.

[85]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[86]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[87]  Joydeep Ghosh,et al.  Cluster Ensembles --- A Knowledge Reuse Framework for Combining Multiple Partitions , 2002, J. Mach. Learn. Res..

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

[89]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

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

[91]  Sergio Gómez,et al.  Hierarchical Multiresolution Method to Overcome the Resolution Limit in Complex Networks , 2012, Int. J. Bifurc. Chaos.

[92]  Jukka-Pekka Onnela,et al.  Taxonomies of networks from community structure. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[94]  F. Luccio,et al.  On the Decomposition of Networks in Minimally Interconnected Subnetworks , 1969 .

[95]  Santo Fortunato,et al.  Community detection in networks: Structural communities versus ground truth , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[96]  Jari Saramäki,et al.  Characterizing the Community Structure of Complex Networks , 2010, PloS one.

[97]  Aristides Gionis,et al.  Proceedings of the sixth ACM international conference on Web search and data mining , 2013, WSDM 2013.

[98]  Dorothea Wagner,et al.  Experiments on comparing graph clusterins , 2006 .

[99]  P. Ronhovde,et al.  Multiresolution community detection for megascale networks by information-based replica correlations. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[100]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, Knowledge and Information Systems.

[101]  Albert-László Barabási,et al.  Bursts: The Hidden Pattern Behind Everything We Do , 2010 .

[102]  Bart Selman,et al.  Tracking evolving communities in large linked networks , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

[104]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

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

[106]  C. Bron,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[107]  Ulrik Brandes,et al.  On Modularity Clustering , 2008, IEEE Transactions on Knowledge and Data Engineering.

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

[109]  Derek Greene,et al.  Normalized Mutual Information to evaluate overlapping community finding algorithms , 2011, ArXiv.

[110]  M. Bousquet-Mélou,et al.  Exactly Solved Models , 2009 .

[111]  Charu C. Aggarwal,et al.  Graph Clustering , 2010, Encyclopedia of Machine Learning and Data Mining.

[112]  Santo Fortunato,et al.  Improving the performance of algorithms to find communities in networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[113]  Tom A. B. Snijders,et al.  Social Network Analysis , 2011, International Encyclopedia of Statistical Science.

[114]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[115]  Albert-László Barabási,et al.  Scale-free networks , 2008, Scholarpedia.

[116]  Mark E. J. Newman,et al.  An efficient and principled method for detecting communities in networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[117]  Mason A. Porter,et al.  Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[118]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[119]  L. Goddard Information Theory , 1962, Nature.

[120]  Deepayan Chakrabarti,et al.  Evolutionary clustering , 2006, KDD '06.

[121]  Peng Zhang,et al.  Comparative definition of community and corresponding identifying algorithm. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[122]  P. Ronhovde,et al.  Local resolution-limit-free Potts model for community detection. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[124]  Yun Chi,et al.  Facetnet: a framework for analyzing communities and their evolutions in dynamic networks , 2008, WWW.

[125]  R. Alba A graph‐theoretic definition of a sociometric clique† , 1973 .

[126]  Peter Forrester Exactly solved models in statistical mechanics and their interplay with classical analysis , 1985 .

[127]  Zheng Wang,et al.  Batch Mode Active Learning for Node Classification in Assortative and Disassortative Networks , 2018, IEEE Access.

[128]  Martin E. Dyer,et al.  The Solution of Some Random NP-Hard Problems in Polynomial Expected Time , 1989, J. Algorithms.

[129]  Guido Caldarelli,et al.  Hierarchical mutual information for the comparison of hierarchical community structures in complex networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[131]  Frank Thomson Leighton,et al.  Graph bisection algorithms with good average case behavior , 1984, Comb..

[132]  Benjamin H. Good,et al.  Performance of modularity maximization in practical contexts. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[133]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[134]  Daniel B. Larremore,et al.  Efficiently inferring community structure in bipartite networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[135]  M. Hastings Community detection as an inference problem. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[137]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[138]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[139]  Santo Fortunato,et al.  Limits of modularity maximization in community detection , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[140]  Konstantin Avrachenkov,et al.  Cooperative Game Theory Approaches for Network Partitioning , 2017, COCOON.

[141]  V. Traag,et al.  Community detection in networks with positive and negative links. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[142]  V A Traag,et al.  Narrow scope for resolution-limit-free community detection. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[143]  Santo Fortunato,et al.  Finding Statistically Significant Communities in Networks , 2010, PloS one.

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

[145]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[146]  D. Garlaschelli,et al.  Community detection for correlation matrices , 2013, 1311.1924.

[147]  A. Moore,et al.  Dynamic social network analysis using latent space models , 2005, SKDD.

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

[149]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[150]  Santo Fortunato,et al.  A benchmark model to assess community structure in evolving networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[152]  Dino Pedreschi,et al.  A classification for community discovery methods in complex networks , 2011, Stat. Anal. Data Min..

[153]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[154]  Andrea Lancichinetti,et al.  Erratum: Community detection algorithms: A comparative analysis [Phys. Rev. E 80, 056117 (2009)] , 2014 .

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

[156]  Vladimir Filkov,et al.  Consensus Clustering Algorithms: Comparison and Refinement , 2008, ALENEX.

[157]  M. Newman Communities, modules and large-scale structure in networks , 2011, Nature Physics.

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

[159]  Tiago P. Peixoto Inferring the mesoscale structure of layered, edge-valued, and time-varying networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[160]  Mark E. J. Newman,et al.  Community detection in networks: Modularity optimization and maximum likelihood are equivalent , 2016, ArXiv.

[161]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[162]  Mason A. Porter,et al.  Social Structure of Facebook Networks , 2011, ArXiv.

[163]  Roger Guimerà,et al.  Missing and spurious interactions and the reconstruction of complex networks , 2009, Proceedings of the National Academy of Sciences.

[164]  Ana L. N. Fred,et al.  Robust data clustering , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[165]  Martin Rosvall,et al.  Compression of flow can reveal overlapping modular organization in networks , 2011, ArXiv.

[166]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

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

[168]  A. Barabasi,et al.  Quantifying social group evolution , 2007, Nature.

[169]  R. Luce,et al.  A method of matrix analysis of group structure , 1949, Psychometrika.

[170]  Martin Rosvall,et al.  Maps of sparse Markov chains efficiently reveal community structure in network flows with memory , 2016, ArXiv.

[171]  Aaron Clauset,et al.  Learning Latent Block Structure in Weighted Networks , 2014, J. Complex Networks.

[172]  Jure Leskovec,et al.  Structure and Overlaps of Ground-Truth Communities in Networks , 2014, TIST.

[173]  T. S. Evans,et al.  Clique graphs and overlapping communities , 2010, ArXiv.

[174]  Marina Meila,et al.  Comparing clusterings: an axiomatic view , 2005, ICML.

[175]  A. Dunker The pacific symposium on biocomputing , 1998 .

[176]  Barbora Micenková,et al.  Clustering attributed graphs: Models, measures and methods , 2015, Network Science.

[177]  Martin Rosvall,et al.  Memory in network flows and its effects on spreading dynamics and community detection , 2013, Nature Communications.

[178]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[179]  F. Guerra Spin Glasses , 2005, cond-mat/0507581.

[180]  Anil K. Jain,et al.  Clustering ensembles: models of consensus and weak partitions , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[181]  A. Mookerjee The Spin Glass , 1996 .

[182]  Cristopher Moore,et al.  Phase transition in the detection of modules in sparse networks , 2011, Physical review letters.

[183]  Luc De Raedt,et al.  Proceedings of the 22nd international conference on Machine learning , 2005 .

[184]  M. Newman Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[185]  Michalis Vazirgiannis,et al.  Clustering and Community Detection in Directed Networks: A Survey , 2013, ArXiv.

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

[187]  V. Latora,et al.  Detecting complex network modularity by dynamical clustering. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[188]  Christophe Ambroise,et al.  Variational Bayesian inference and complexity control for stochastic block models , 2009, 0912.2873.

[189]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[190]  M. Newman,et al.  Robustness of community structure in networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[191]  R. Lambiotte,et al.  Line graphs, link partitions, and overlapping communities. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[192]  Philip S. Yu,et al.  Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics , 2012, KDD 2012.

[193]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[194]  Mingwei Leng,et al.  Active Semi-supervised Community Detection Algorithm with Label Propagation , 2013, DASFAA.

[195]  Chid Apte,et al.  Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Diego, CA, USA, August 21-24, 2011 , 2011, KDD.

[196]  Yihong Gong,et al.  A Bayesian Approach Toward Finding Communities and Their Evolutions in Dynamic Social Networks , 2009, SDM.

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

[198]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[199]  Elchanan Mossel,et al.  Spectral redemption in clustering sparse networks , 2013, Proceedings of the National Academy of Sciences.

[200]  R. J. Mokken,et al.  Cliques, clubs and clans , 1979 .

[201]  Haijun Zhou Network landscape from a Brownian particle's perspective. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[202]  Pan Zhang,et al.  Evaluating accuracy of community detection using the relative normalized mutual information , 2015, ArXiv.

[203]  Ernesto Estrada,et al.  The Structure of Complex Networks: Theory and Applications , 2011 .

[204]  Leto Peel,et al.  Active discovery of network roles for predicting the classes of network nodes , 2013, J. Complex Networks.

[205]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[206]  Ernesto Estrada,et al.  A First Course in Network Theory , 2015 .

[207]  B. Bollobás The evolution of random graphs , 1984 .

[208]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[209]  Gesine Reinert,et al.  Estimating the number of communities in a network , 2016, Physical review letters.

[210]  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.

[211]  Pang-Ning Tan,et al.  Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II , 2012 .

[212]  Mark E. J. Newman,et al.  Structure and inference in annotated networks , 2015, Nature Communications.

[213]  P. Latouche,et al.  Model selection and clustering in stochastic block models based on the exact integrated complete data likelihood , 2015 .

[214]  M. Newman Community detection in networks: Modularity optimization and maximum likelihood are equivalent , 2016, Physical review. E.

[215]  Martin Rosvall,et al.  Modelling sequences and temporal networks with dynamic community structures , 2015, Nature Communications.

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

[217]  John Scott Social Network Analysis , 1988 .

[218]  Boleslaw K. Szymanski,et al.  Overlapping community detection in networks: The state-of-the-art and comparative study , 2011, CSUR.

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

[220]  Coenraad Bron,et al.  Finding all cliques of an undirected graph , 1973 .

[221]  Yun Chi,et al.  Evolutionary spectral clustering by incorporating temporal smoothness , 2007, KDD '07.

[222]  Sergio Gómez,et al.  Detecting communities of triangles in complex networks using spectral optimization , 2010, Comput. Commun..

[223]  Alex Arenas,et al.  Analysis of the structure of complex networks at different resolution levels , 2007, physics/0703218.

[224]  Muhammad Aamir Cheema,et al.  Database Systems for Advanced Applications , 2015, Lecture Notes in Computer Science.

[225]  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.

[226]  Tiago P. Peixoto Hierarchical block structures and high-resolution model selection in large networks , 2013, ArXiv.

[227]  Haijun Zhou Distance, dissimilarity index, and network community structure. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[228]  Marina Meila,et al.  An Experimental Comparison of Model-Based Clustering Methods , 2004, Machine Learning.

[229]  M. Cugmas,et al.  On comparing partitions , 2015 .