Post-processing hierarchical community structures: Quality improvements and multi-scale view

Dense sub-graphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Most existing community detection algorithms produce a hierarchical structure of communities and seek a partition into communities that optimizes a given quality function. We propose new methods to improve the results of any of these algorithms. First we show how to optimize a general class of additive quality functions (containing the modularity, the performance, and a new similarity based quality function which we propose) over a larger set of partitions than the classical methods. Moreover, we define new multi-scale quality functions which make it possible to detect different scales at which meaningful community structures appear, while classical approaches find only one partition.

[1]  Ron Shamir,et al.  A clustering algorithm based on graph connectivity , 2000, Inf. Process. Lett..

[2]  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.

[3]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[4]  Massimo Marchiori,et al.  Method to find community structures based on information centrality. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[6]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[7]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[9]  S. Strogatz.  Exploring complex networks , 2001, Nature.

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

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

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

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

[14]  Ulrik Brandes,et al.  Network Analysis: Methodological Foundations (Lecture Notes in Computer Science) , 2005 .

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

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

[17]  Santosh S. Vempala,et al.  On clusterings-good, bad and spectral , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[18]  Philippe Flajolet,et al.  An introduction to the analysis of algorithms , 1995 .

[19]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

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

[21]  M. A. Muñoz,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Detecting network communities: a new systematic and efficient algorithm , 2004 .