Statistical significance across multiple optimization models for community partition

The study of community structure is an important problem in a wide range of applications, which can help us understand the real network system deeply. However, due to the existence of random factors and error edges in real networks, how to measure the significance of community structure efficiently is a crucial question. In this paper, we present a novel statistical framework computing the significance of community structure across multiple optimization methods. Different from the universal approaches, we calculate the similarity between a given node and its leader and employ the distribution of link tightness to derive the significance score, instead of a direct comparison to a randomized model. Based on the distribution of community tightness, a new “p-value” form significance measure is proposed for community structure analysis. Specially, the well-known approaches and their corresponding quality functions are unified to a novel general formulation, which facilitates in providing a detailed comparison across them. To determine the position of leaders and their corresponding followers, an efficient algorithm is proposed based on the spectral theory. Finally, we apply the significance analysis to some famous benchmark networks and the good performance verified the effectiveness and efficiency of our framework.

[1]  Xiang-Sun Zhang,et al.  Potts model based on a Markov process computation solves the community structure problem effectively , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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

[5]  Lin Wang,et al.  Spatial epidemiology of networked metapopulation: an overview , 2014, bioRxiv.

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

[7]  Cristopher Moore,et al.  Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Andrew B. Nobel,et al.  A Testing Based Extraction Algorithm for Identifying Significant Communities in Networks , 2013, ArXiv.

[9]  M. Hastings.  Community detection as an inference problem. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Réka Albert,et al.  Near linear time algorithm to detect community structures in large-scale networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Chris H Wiggins,et al.  Bayesian approach to network modularity. , 2007, Physical review letters.

[12]  Sune Lehmann,et al.  Link communities reveal multiscale complexity in networks , 2009, Nature.

[13]  Konstantin Avrachenkov,et al.  Cooperative Game Theory Approaches for Network Partitioning , 2017, COCOON.

[14]  M. Newman,et al.  Robustness of community structure in networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  M. Barber,et al.  Detecting network communities by propagating labels under constraints. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  J. Kertész,et al.  On the equivalence of the label propagation method of community detection and a Potts model approach , 2008, 0803.2804.

[17]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[18]  Shihua Zhang,et al.  Identification of overlapping community structure in complex networks using fuzzy c-means clustering , 2007 .

[19]  Yong Wang,et al.  Community structure detection based on Potts model and network's spectral characterization , 2012 .

[20]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Cristopher Moore,et al.  Phase transition in the detection of modules in sparse networks , 2011, Physical review letters.

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

[23]  Hao Wang,et al.  Measuring robustness of community structure in complex networks , 2014, ArXiv.

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

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

[26]  E A Leicht,et al.  Mixture models and exploratory analysis in networks , 2006, Proceedings of the National Academy of Sciences.

[27]  Santo Fortunato,et al.  Finding Statistically Significant Communities in Networks , 2010, PloS one.

[28]  P. Pin,et al.  Assessing the relevance of node features for network structure , 2008, Proceedings of the National Academy of Sciences.

[29]  Xiang-Sun Zhang,et al.  Analysis of stability of community structure across multiple hierarchical levels , 2015, ArXiv.

[30]  Cristopher Moore,et al.  Scalable detection of statistically significant communities and hierarchies, using message passing for modularity , 2014, Proceedings of the National Academy of Sciences.

[31]  Hui-Jia Li,et al.  Social significance of community structure: Statistical view , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[33]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.