Community Discovery Methods for Complex Networks

21 Jan 2010 08:36

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Given: a network, especially a large one, directed or not, weighted or not. Desired: a sensible decomposition of the graph into sub-graphs, where in some reasonable sense the nodes in each sub-graph have more to do with each other than with outsiders, i.e., form communities. This is also called "module detection".

This seems like a really useful idea to apply to problems I'm interested in, in neural synchronization; also a place where there could stand to be more interchange between statistics and complex-network-wallahs.

Some of the methods in this area remind me of stuff Christopher Alexander did in his 1964 book Notes on the Synthesis of Form, but it's been a long time since I read that, so my memory may be faulty.

See also: Ecology; Neuroscience; Signal Transduction, Gene Regulation and Control of Metabolism; Social Networks; Sociology of Science; Statistical Mechanics; Synchronization

Recommended, big picture:
• Peter J. Bickel and Aiyou Chen, "A nonparametric view of network models and Newman-Girvan and other modularities", Proceedings of the National Academy of Sciences (USA) 106 (2009): 21068--21073
• Michelle Girvan and M. E. J. Newman, "Community structure in social and biological networks," cond-mat/0112110 = Proceedings of the National Academy of Sciences (USA) 99 (2002): 7821--7826
• Jake M. Hofman, Chris H. Wiggins, "A Bayesian Approach to Network Modularity", arxiv:0709.3512 [For "Bayesian", read "smoothed maximum likelihood". But nonetheless: cool.]
• M. E. J. Newman
  • "Modularity and community structure in networks", physics/0602124 = Proceedings of the National Academy of Sciences (USA) 103 (2006): 87577--8582
  • "Finding community structure in networks using the eigenvectors of matrices", Physical Review E 74 (2006): 036104 = physics/0605087
• M. E. J. Newman and Michelle Girvan
  • "Mixing patterns and community structure in networks", cond-mat/0210146
  • "Finding and evaluating community structure in networks", Physical Review E 69 (2003): 026113 = cond-mat/0308217

Recommended, close-ups:
• Aaron Clauset, "Finding local community structure in networks", physics/0503036 = Physical Review E 72 (2005): 026132 [Clever; but then, Aaron is clever.]
• Aaron Clauset, M. E. J. Newman and Cristopher Moore, "Finding Community Structure in Very Large Networks", cond-mat/0408187 = Physical Review E 70 (2004): 066111
• J.-J. Daudin, F. Picard and S. Robin, "A Mixture Model for Random Graphs", Statistics and Computing 18 (2008): 173--183
• Roger Guimera, Marta Sales-Pardo and Luis A. N. Amaral, "Modularity from Fluctuations in Random Graphs", cond-mat/0403660 = Physical Review E 70 (2004): 025101
• Andrea Lancichinetti, Santo Fortunato, Janos Kertesz, "Detecting the overlapping and hierarchical community structure of complex networks", arxiv:0802.1218 [An interesting approach, but not quite as novel as they claim --- cf. Reichardt and Bornholdt --- and I'd really like to see more evidence of superior accuracy and/or robustness]
• E. A. Leicht, M. E. J. Newman, "Community structure in directed networks", arxiv:0709.4500
• Jörg Reichardt and Stefan Bornholdt [Code is available by e-mail from Reichardt, who was very helpful to me when I needed to implement their algorithm.]
  • "Detecting Fuzzy Community Structures in Complex Networks with a Potts Model", Physical Review Letters 93 (2004): 218701 = cond-mat/0402349
  • "Statistical Mechanics of Community Detection", cond-mat/0603718 = Physical Review E 74 (2006): 016110
  • "Clustering of sparse data via network communities — a prototype study of a large online market", Journal of Statistical Mechanics: Theory and Experiment (2007): P06016
• Jörg Reichardt and Douglas R. White, "Role models for complex networks", arxiv:0708.0958 [Discussion]
• M. Sales-Pardo, R. Guimera, A. Moreira, L. Amaral, "Extracting the hierarchical organization of complex systems", arxiv:0705.1679

Modesty forbids me to recommend:
• CRS, Marcelo F. Camperi and Kristina Lisa Klinkner, "Discovering Functional Communities in Dynamical Networks", q-bio.NC/0609008

To read:
• Edoardo M. Airoldi, David M. Blei, Stephen E. Fienberg and Eric P. Xing, "Mixed membership stochastic blockmodels", arxiv:0705.4485
• Nelson Augusto Alves, "Unveiling community structures in weighted networks", physics/0703087
• Leonardo Angelini, Stefano Boccaletti, Daniele Marinazzo, Mario Pellicoro, and Sebastiano Stramaglia, "Fast identification of network modules by optimization of ratio association", cond-mat/0610182
• L. Angelini, D. Marinazzo, M. Pellicoro and S. Stramaglia, "Natural clustering: the modularity approach", cond-mat/0607643
• A. Arenas, J. Duch, A. Fernandez, S. Gomez, "Size reduction of complex networks preserving modularity", physics/0702015 [Do you really need all those links? Wouldn't your life be simpler if you could just ignore some of them?]
• Alex Arenas, Alberto Fernandez, Sergio Gomez, "Multiple resolution of the modular structure of complex networks", physics/0703218
• Alex Arenas, Alberto Fernandez, Santo Fortunato, Sergio Gomez, "Motif-based communities in complex networks", arxiv:0710.0059
• Jim Bagrow and Erik Bollt, "A Local Method for Detecting Communities", cond-mat/0412482
• James Bagrow, Erik Bollt, Luciano da F. Costa, "Network Structure Revealed by Short Cycles", cond-mat/0612502
• Jonathan W. Berry, Bruce Hendrickson, Randall A. LaViolette, Cynthia A. Phillips, "Tolerating the Community Detection Resolution Limit with Edge Weighting", arxiv:0903.1072 [I have to say that their abstract sounds like a recipe for over-fitting, but I haven't read the paper so that could be totally unfair.]
• S. Boccaletti, M. Ivanchenko, V. Latora, A. Pluchino and A. Rapisarda, "Dynamical clustering methods to find community structures", physics/0607179
• Michael James Bommarito II, Daniel Martin Katz, Jon Zelner, "On the Stability of Community Detection Algorithms on Longitudinal Citation Data", arxiv:0908.0449
• U. Brandes, D. Delling, M. Gaertler, R. Goerke, M. Hoefer, Z. Nikoloski, and D. Wagner, "Maximizing Modularity is hard", physics/0608255 [i.e., maximizing Newman's Q is NP hard. I haven't read beyond the abstract yet, so I don't know if they address the question of what makes it hard in the hard cases, and whether those are properties we should expect to see in real-world networks. Conceivably, actual social networks are, on average, easy to modularize...]
• Andrea Capocci, Vito D. P. Servedio, Guido Caldarelli, Francesca Colaiori, "Detecting communities in large networks", cond-mat/0402499
• Horacio Castellini and Lilia Romanelli, "Social network from communities of electronic mail", nlin.CD/0509021
• Sanjeev Chauhan, Michelle Girvan and Edward Ott, "", Physical Review E 80 (2009): 056114
• Leon Danon, Albert Díaz-Guilera, and Alex Arenas, "The effect of size heterogeneity on community identification in complex networks", Journal of Statistical Mechanics: Theory and Experiment (2006): P11010 = physics/0601144
• Leon Danon, Albert Díaz-Guilera, Jordi Duch and Alex Arenas, "Comparing community structure identification", Journal of Statistical Mechanics: Theory and Experiment (2005): P09008 = cond-mat/0505245
• Jordi Duch and Alex Arenas, "Community detection in complex networks using extremal optimization", Physical Review E 72 (2005): 027104
• Illes J. Farkas, Daniel Abel, Gergely Palla, Tamas Vicsek, "Weighted network modules", cond-mat/0703706
• S. Feldt, J. Waddell, V. L. Hetrick, J. D. Berke, and M. Zochowski, "Functional clustering algorithm for the analysis of dynamic network data", Physical Review E 79 (2009): 056104
• Daniel J. Fenn, Mason A. Porter, Mark McDonald, Stacy Williams, Neil F. Johnson, Nick S. Jones, "Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis", arxiv:0811.3988
• Daniel J. Fenn, Mason A. Porter, Peter J. Mucha, Mark McDonald, Stacy Williams, Neil F. Johnson, Nick S. Jones, "Dynamical Clustering of Exchange Rates", arxiv:0905.4912
• Sam Field, Kenneth A. Frank, Kathryn Schiller, Catherine Riegle-Crumb and Chandra Muller, "Identifying positions from affiliation networks: Preserving the duality of people and events", Social Networks 28 (2006): 97--123
• G. W. Flake, S. R. Lawrence, C. L. Giles and F. M. Coetzee, "Self-organization and identification of Web communities", IEEE Computer 36 (2002): 66--71
• Santo Fortunato, "Community detection in graphs", arxiv:0906.0612
• Santo Fortunato and Marc Bathélemy, "Resolution limit in community detection", physics/0607100 = cite>Proceedings of the National Academy of Sciences (USA) 104 (2007): 36--41
• Santo Fortunato and Claudio Castellano, "Community Structure in Graphs", arxiv:0712.2716 [Review paper; thanks to Ed Vielmetti for the pointer]
• Santo Fortunato, Vito Latora and Massimo Marchiori, "A Method to Find Community Structures Based on Information Centrality", cond-mat/0402522
• Kenneth A. Frank, "Identifying Cohesive Subgroups", Social Networks 17 (1995): 27--56
• David Gfeller, Jean-Cédric Chappelier, and Paolo De Los Rios, "Finding instabilities in the community structure of complex networks", Physical Review E 72 (2005): 056135
• Rumi Ghosh, Kristina Lerman, "Structure of Heterogeneous Networks", arxiv:0906.2212
• V. Gol'dshtein and G. A. Koganov, "An indicator for community structure", physics/0607159
• Benjamin H. Good, Yves-Alexandre de Montjoye, Aaron Clauset, "The performance of modularity maximization in practical contexts", arxiv:0910.0165
• Mark S. Handcock, Adrian E. Raftery and Jeremy Tantrum, "Model-Based Clustering for Social Networks" Journal of the Royal Statistical Society A 170 (2007): 301--354 [PDF preprint]
• M. B. Hastings, "Community detection as an inference problem", Physical Review E 74 (2006): 035102 = cond-mat/0604429
• Erik Holmström, Nicolas Bock and Joan Brännlund, "Density Analysis of Network Community Divisions", cond-mat/0608612
• I. Ispolatov, I. Mazo, A. Yuryev, "Finding mesoscopic communities in sparse networks", q-bio.MN/0512038 = Journal of Statistical Mechanics (2006): P09014
• Brian Karrer, Elizaveta Levina, M. E. J. Newman, "Robustness of community structure in networks", arxiv:0709.2108
• Jussi M. Kumpula, Jari Saramaki, Kimmo Kaski, and Janos Kertesz, "Resolution limit in complex network community detection with Potts model approach",cond-mat/0610370
• Andrea Lancichinetti, Santo Fortunato
  • "Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities", arxiv:0904.3940
  • "Community detection algorithms: A comparative analysis", Physical Review E 80 (2009): 056117
• Pierre Latouche, Etienne Birmelé, Christophe Ambroise, "Overlapping Stochastic Block Models", arxiv:0910.2098
• Sune Lehmann, Martin Schwartz, Lars Kai Hansen, "Bi-clique Communities", arxiv:0710.4867
• Michele Leone, Sumedha, Martin Weigt, "Clustering by soft-constraint affinity propagation: Applications to gene-expression data", arxiv:0705.2646
• Jure Leskovec, Kevin J. Lang, Anirban Dasgupta and Michael W. Mahoney, "Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters", arxiv:0810.1355
• Ian X.Y. Leung, Pan Hui, Pietro Lio', Jon Crowcroft, "Towards Real Time Community Detection in Large Networks", arxiv:0808.2633
• Claire P. Massen, Jonathan P. K. Doye, "Thermodynamics of Community Structure", cond-mat/0610077
• A. D. Medus and C. O. Dorso, "Alternative approach to community detection in networks", Physical Review E 79 (2009): 066111
• Peter J. Mucha, Thomas Richardson, Kevin Macon, Mason A. Porter, Jukka-Pekka Onnela, "Community Structure in Time-Dependent, Multiscale, and Multiplex Networks", arxiv:0911.1824
• Stefanie Muff, Francesco Rao, and Amedeo Caflisch, "Local modularity measure for network clusterizations", Physical Review E 72 (2005): 056107
• Andreas Noack, "Modularity clustering is force-directed layout", arxiv:0807.4052
• Gergely Palla, Imre Derenyi, Illes Farkas and Tamas Vicsek, "Uncovering the overlapping community structure of complex networks in nature and society", Nature 435 (2005): 814--818 = physics/0506133
• Gergely Palla, Illes J. Farkas, Peter Pollner, Imre Derenyi, Tamas Vicsek, "Directed network modules", physics/0703248
• Nicolas Pissard and Houssem Assadi, "Detecting overlapping communities in linear time with P&A algorithm", physics/0509254
• Pascal Pons, "Post-Processing Hierarchical Community Structures: Quality Improvements and Multi-scale View", cs.DS/0608050
• Mason A. Porter, Jukka-Pekka Onnela, Peter J. Mucha, "Communities in Networks", arxiv:0902.3788
• Josep M. Pujol, Javier Béjar, and Jordi Delgado, "Clustering algorithm for determining community structure in large networks", Physical Review E 74 (2006): 016107
• Francisco A. Rodrigues, Gonzalo Travieso, Luciano da F. Costa, "Fast Community Identification by Hierarchical Growth", physics/0602144
• Huaijun Qiu and Edwin R. Hancock, "Graph matching and clustering using spectral partitions", Pattern Recognition 39 (2006): 22--34 [In this context, for the ideas on hierarchical decomposition, which sounds like it might work for community discovery, if in fact it's not equivalent to some existing community-discovery algorithm.]
• Usha Nandini Raghavan, Reka Albert, Soundar Kumara, "Near linear time algorithm to detect community structures in large-scale networks", arxiv:0709.2938 ["every node is initialized with a unique label and at every step each node adopts the label that most of its neighbors currently have"]
• Jörg Reichardt and Stefan Bornholdt, "When are networks truly modular?", cond-mat/0606220
• Jörg Reichardt and Michele Leone, "(Un)detectable cluster structure in sparse networks", arxiv:0711.1452
• Martin Rosvall and Carl T. Bergstrom
  • "An information-theoretic framework for resolving community structure in complex networks", physics/0612035 [Or, MDL to the rescue!]
  • "Maps of random walks on complex networks reveal community structure", Proceedings of the National Academy of Sciences (USA) 105 (2008): 1118--1123
• Erin N. Sawardecker, Marta Sales-Pardo, Luís A. Nunes Amaral, "Detection of node group membership in networks with group overlap", arxiv:0812.1243
• Chayant Tantipathananandh, Tanya Berger-Wolf and David Kempe, "A Framework For Community Identification in Dynamic Social Networks" [PDF]
• Joshua R. Tyler, Dennis M. Wilkinson and Bernardo A. Huberman, "Email as Spectroscopy: Automated Discovery of Community Structure within Organizations," cond-mat/0303264
• I. Vragovic and E. Louis, "Network community structure and loop coefficient method", Physical Review E 74 (2006): 016105
• Matthew L. Wallace, Yves Gingras, Russell Duhon, "A new approach for detecting scientific specialties from raw cocitation networks", arxiv:0807.4903
• Huijie Yang, Wenxu Wang, Tao Zhou, Binghong ang and Fangcui Zhao, "Reconstruct the Hierarchical Structure in a Complex Network", physics/0508026 ["Based upon the eigenvector centrality (EC) measure, a method is proposed to reconstruct the hierarchical structure of a complex network. It is tested on the Santa Fe Institute collaboration network, whose structure is well known."]
• Hugo Zanghi, Franck Picard, Vincent Miele, Christophe Ambroise, "Strategies for Online Inference of Model-Based Clustering in large Networks", arxiv:0910.2034
• Haijun Zhou
  • "Distance, dissimilarity index, and network community structure," physics/0302032
  • "Network Landscape from a Brownian Particle's Perspective," physics/0302030
• Etay Ziv, Manuel Middendorf and Chris Wiggins, "An Information-Theoretic Approach to Network Modularity", q-bio.QM/0411033

To finish writing:
• "Functional Community Discovery II"