Fast Multi-Scale Detection of Relevant Communities

Nowadays, networks are almost ubiquitous. In the past decade, community detection received an increasing interest as a way to uncover the structure of networks by grouping nodes into communities more densely connected internally than externally. Yet most of the effective methods available do not consider the potential levels of organisation, or scales, a network may encompass and are therefore limited. In this paper we present a method compatible with global and local criteria that enables fast multi-scale community detection. The method is derived in two algorithms, one for each type of criterion, and implemented with 6 known criteria. Uncovering communities at various scales is a computationally expensive task. Therefore this work puts a strong emphasis on the reduction of computational complexity. Some heuristics are introduced for speed-up purposes. Experiments demonstrate the efficiency and accuracy of our method with respect to each algorithm and criterion by testing them against large generated multi-scale networks. This study also offers a comparison between criteria and between the global and local approaches.

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

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

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

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

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

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

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

[8]  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.

[9]  Chris Hankin,et al.  Multi-scale Community Detection using Stability as Optimisation Criterion in a Greedy Algorithm , 2011, KDIR.

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

[11]  S.,et al.  An Efficient Heuristic Procedure for Partitioning Graphs , 2022 .

[12]  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.

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

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

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

[16]  V. Strassen.  Gaussian elimination is not optimal , 1969 .

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

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

[19]  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.