Community Discovery Methods for Complex Networks

04 Apr 2012 13:55

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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 [See under Graph Limits and Infinite Exchangeable Arrays]
• 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:
• Edoardo M. Airoldi, David M. Blei, Stephen E. Fienberg and Eric P. Xing, "Mixed membership stochastic blockmodels", arxiv:0705.4485
• Aaron Clauset, "Finding local community structure in networks", Physical Review E 72 (2005): 026132, physics/0503036 [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
• Aurelien Decelle, Florent Krzakala, Cristopher Moore and Lenka Zdeborova
  • "Phase transition in the detection of modules in sparse networks", Physical Review Letters 107 (2011): 065701, arxiv:1102.1182
  • "Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications", Physical Review E 84 (2011): 066106, arxiv:1109.3041
• 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
• J. A. Henderson and P. A. Robinson, "Geometric Effects on Complex Network Structure in the Cortex", Physical Review Letters 107 (2011): 018102
• Brian Karrer, M. E. J. Newman, "Stochastic blockmodels and community structure in networks", Physical Review 83 (2011): 016107, arxiv:1008.3926
• 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
• Mahendra Mariadassou, Stéphane Robin, and Corinne Vacher, "Uncovering latent structure in valued graphs: A variational approach", Annals of Applied Statistics 4 (2010): 715-774
• 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
• 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]
• 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
• M. Sales-Pardo, R. Guimera, A. Moreira, L. Amaral, "Extracting the hierarchical organization of complex systems", arxiv:0705.1679
• Yunpeng Zhao, Elizaveta Levina and Ji Zhu, "Community extraction for social networks", arxiv:1005.3265

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:
• Yong-Yeol Ahn, James P. Bagrow and Sune Lehmann, "Link communities reveal multiscale complexity in networks", Nature 455 (2010): 761--764, arxiv:0903.3178 [Lehmann's blog-post on this]
• 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
• Alex Arenas, Javier Borge-Holthoefer, Sergio Gomez, Gorka Zamora-Lopez, "Optimal map of the modular structure of complex networks", New Journal of Physics 12 (2010): 053009, arxiv:0911.2651
• 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
• Sanjeev Arora, Rong Ge, Sushant Sachdeva, Grant Schoenebeck, "Finding Overlapping Communities in Social Networks: Toward a Rigorous Approach", arxiv:1112.1831 [By "rigorous", they mean "rigorous analysis of the algorithm", not, e.g., a statistically or scientifically rigorous approach.]
• Jim Bagrow and Erik Bollt, "A Local Method for Detecting Communities", PHysical Review E 72 (2005): 046108, cond-mat/0412482
• James Bagrow, Erik Bollt, Luciano da F. Costa, "Network Structure Revealed by Short Cycles", cond-mat/0612502
• Brian Ball, Brian Karrer, M. E. J. Newman, "An efficient and principled method for detecting communities in networks", arxiv:1104.3590
• Michael J. Barber, John W. Clark, "Detecting network communities by propagating labels under constraints", Physical Review E 80 (2009): 026129, arxiv:0903.3138
• 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
• Marianna Bolla, "Penalized versions of the Newman-Girvan modularity and their relation to normalized cuts and k-means clustering", Physical Review E 84 (2011): 016108
• 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
• Federica Cerina, Vincenzo De Leo, Marc Barthelemy, Alessandro Chessa, "Spatial correlations in attribute communities", arxiv:1112.3308
• Antoine Channarond, Jean-Jacques Daudin, Stéphane Robin, "Classification and estimation in the Stochastic Block Model based on the empirical degrees", arxiv:1110.6517
• Sanjeev Chauhan, Michelle Girvan and Edward Ott, "", Physical Review E 80 (2009): 056114
• David S. Choi, Patrick J. Wolfe, Edoardo M. Airoldi, "Stochastic blockmodels with growing number of classes", arxiv:1011.4644
• Gennaro Cordasco, Luisa Gargano, "Community Detection via Semi-Synchronous Label Propagation Algorithms", arxiv:1103.4550
• 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
• Bhaskar DasGupta, Devendra Desai, "On the Complexity of Newman's Community Finding Approach for Biological and Social Networks", arxiv:1102.0969
• Jordi Duch and Alex Arenas, "Community detection in complex networks using extremal optimization", Physical Review E 72 (2005): 027104
• Lilia Efimova and Stephanie Hendrick, "In search for a virtual settlement: An exploration of weblog community boundaries" [PDF reprint]
• 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
• Adrien Friggeri, Guillaume Chelius, Eric Fleury, "Triangles to Capture Social Cohesion", arxiv:1107.3231
• 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
• Sergio Gomez, Pablo Jensen, Alex Arenas, "Analysis of community structure in networks of correlated data", Physical Review E 80 (2009): 016114, arxiv:0812.2030
• Benjamin H. Good, Yves-Alexandre de Montjoye, Aaron Clauset, "The performance of modularity maximization in practical contexts", arxiv:0910.0165
• Clara Granell, Sergio Gomez, Alex Arenas, "Mesoscopic analysis of networks: applications to exploratory analysis and data clustering", arxiv:1101.1811
• 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
• Frank Havemann, Michael Heinz, Alexander Struck, Jochen Gläser, "Identification of Overlapping Communities by Locally Calculating Community-Changing Resolution Levels", Journal of Statistical Mechanics: Theory and Experiment (2011): P01023, arxiv:1008.1004
• Qirong Ho, Le Song, Eric Xing, "Evolving Cluster Mixed-Membership Blockmodel for Time-Evolving Networks", AISTATS 2011
• Qirong Ho, Ankur Parikh, Le Song, Eric Xing, "Multiscale Community Blockmodel for Network Exploration", AISTATS 2011
• Erik Holmström, Nicolas Bock and Joan Brännlund, "Density Analysis of Network Community Divisions", cond-mat/0608612
• Yanqing Hu, Yuchao Nie, Hua Yang, Jie Cheng, Ying Fan, and Zengru Di, "Measuring the significance of community structure in complex networks", Physical Review E 82 (2010): 066106
• 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
• Alireza Khadivi, Ali Ajdari Rad, and Martin Hasler, "Network community-detection enhancement by proper weighting", Physical Review E 83 (2011): 046104
• Jussi M. Kumpula, Jari Saramaki, Kimmo Kaski, and Janos Kertesz, "Resolution limit in complex network community detection with Potts model approach",cond-mat/0610370
• Darong Lai, Christine Nardini and Hongtao Lu, "Partitioning networks into communities by message passing", Physical Review E 83 (2011): 016115
• Renaud Lambiotte, "Multi-scale Modularity in Complex Networks", arxiv:1004.4268
• 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
  • "Limits of modularity maximization in community detection", Physical Review E 84 (2011): 066122, arxiv:1107.1155
  • "Consensus clustering in complex networks", arxiv:1203.6093
• Andrea Lancichinetti, Filippo Radicchi, Jose' Javier Ramasco, Santo Fortunato, "Finding statistically significant communities in networks", arxiv:1012.2363
• Pierre Latouche, Etienne Birmelé, and Christophe Ambroise, "Overlapping stochastic block models with application to the French political blogosphere", Annals of Applied Statistics 5 (2011): 309--336, 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
• D. Liu, N. Blenn, P. Van Mieghem, "Modeling Social Networks with Overlapping Communities Using Hypergraphs and Their Line Graphs", arxiv:1012.2774
• Claire P. Massen, Jonathan P. K. Doye, "Thermodynamics of Community Structure", cond-mat/0610077
• Aaron F. McDaid, Derek Greene, Neil Hurley, "Normalized Mutual Information to evaluate overlapping community finding algorithms", arxiv:1110.2515
• Aaron F. McDaid, Thomas Brendan Murphy, Nial Friel, Neil J Hurley, "Clustering in networks with the collapsed Stochastic Block Model", arxiv:1203.3083
• A. D. Medus and C. O. Dorso, "Alternative approach to community detection in networks", Physical Review E 79 (2009): 066111
• Atieh Mirshahvalad, Johan Lindholm, Mattias Derlen, Martin Rosvall, "Significant communities in large sparse networks", arxiv:1110.0305
• Bivas Mitra, Lionel Tabourier, Camille Roth, "Intrinsically Dynamic Network Communities", arxiv:1111.2018
• Stefanie Muff, Francesco Rao, and Amedeo Caflisch, "Local modularity measure for network clusterizations", Physical Review E 72 (2005): 056107
• Takashi Nishikawa, Adilson E. Motter, "Discovering Network Structure Beyond Communities", arxiv:1111.6115
• Andreas Noack, "Modularity clustering is force-directed layout", Physical Review E 79 (2009): 026102 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
• Carlo Piccardi, "Finding and testing network communities by lumped Markov chains", arxiv:1106.0596
• 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
• Ioannis Psorakis, Stephen Roberts, Ben Sheldon, "Efficient Bayesian Community Detection using Non-negative Matrix Factorisation", arxiv:1009.2646
• 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.]
• Filippo Radicchi, Andrea Lancichinetti and José J. Ramasco, "Combinatorial approach to modularity", Physical Review E 82 (2010): 026102, arxiv:1004.5283
• 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"]
• Anil Raj, Chris H. Wiggins, "An information-theoretic derivation of min-cut based clustering", arxiv:0811.4208 [I'm not sure if "explained over drinks" counts as "heard the talk"]
• 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
• Fergal Reid, Aaron McDaid, Neil Hurley, "Partitioning Breaks Communities", arxiv:1105.5344
• Thomas Richardson, Peter J. Mucha, Mason A. Porter, "Spectral tripartitioning of networks", Physical Review E 80 (2009): 036111, arxiv:0812.2852
• Daniel M. Romero, Chenhao Tan, Johan Ugander, "Social-Topical Affiliations: The Interplay between Structure and Popularity", arxiv:1112.1115
• Peter Ronhovde and Zohar Nussinov, "Local resolution-limit-free Potts model for community detection", Physical Review E 81 (2010): 046114, arxiv:0812.1072
• Ryan Rossi, Brian Gallagher, Jennifer Neville, Keith Henderson, "Role-Dynamics: Fast Mining of Large Dynamic Networks", arxiv:1203.2200
• Somwrita Sarkar and Andy Dong, "Community detection in graphs using singular value decomposition", Physical Review E 83 (2011): 046114
• Erin N. Sawardecker, Marta Sales-Pardo, Luís A. Nunes Amaral, "Detection of node group membership in networks with group overlap", arxiv:0812.1243
• Michael T. Schaub, Renaud Lambiotte, Mauricio Barahona, "Coding of Markov dynamics for multiscale community detection in complex networks", arxiv:1109.6642
• Devavrat Shah, Tauhid Zaman, "Community Detection in Networks: The Leader-Follower Algorithm", arxiv:1011.0774
• Janne Sinkkonen, Janne Aukia, Samuel Kaski, "Component models for large networks", arxiv:0803.1628
• Tom A.B. Snijders and Krzysztof Nowicki, "Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure", Journal of Classification 14 (1997): 75--100
• Matthew Steen, Satoru Hayasaka, Karen Joyce, Paul Laurienti, "Assessing the consistency of community structure in complex networks", Physical Review E 84 (2011): 016111, arxiv:1106.0041
• S. Stramaglia, Guo-Rong Wu, M. Pellicoro, D. Marinazzo, "Expanding the Transfer Entropy to Identify Information Subgraphs in Complex Systems", arxiv:1203.3037
• Daniel L. Sussman, Minh Tang, Donniell E. Fishkind, Carey E. Priebe, "A consistent dot product embedding for stochastic blockmodel graphs", arxiv:1108.2228
• Chayant Tantipathananandh, Tanya Berger-Wolf and David Kempe, "A Framework For Community Identification in Dynamic Social Networks" [PDF]
• Gergely Tibely, Marton Karsai, Lauri Kovanen, Kimmo Kaski, Janos Kertesz, Jari Saramaki, "Communities and beyond: mesoscopic analysis of a large social network with complementary methods", Physical Review E 83 (2011): 056125, arxiv:1006.0418
• V.A. Traag, P. Van Dooren, Y. Nesterov, "Narrow scope for resolution-free community detection", arxiv:1104.3083
• 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
• Haoran Wen, E. A. Leicht and Raissa M. D'Souza, "Improving community detection in networks by targeted node removal", Physical Review E 83 (2011): 016114
• 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
• Weituo Zhang, Chjan C. Lim, "The Concentration and Stability of the Community Detecting Functions on Random Networks", arxiv:1203.5974
• Yunpeng Zhao, Elizaveta Levina, Ji Zhu, "On Consistency of Community Detection in Networks", arxiv:1110.3854
• 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"