Community Discovery Methods for Complex Networks

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.

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

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

CRS, Marcelo F. Camperi and Kristina Lisa Klinkner, "Discovering Functional Communities in Dynamical Networks", q-bio.NC/0609008

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

"Functional Community Discovery II"

Notebooks

Community Discovery Methods for Complex Networks