Fuzzy communities and the concept of bridgeness in complex networks.

By Tamás Nepusz, A. Petróczi, László Négyessy, F. Bazsó. Physical review. E, Statistical, nonlinear, and soft matter physics, 2007

426 citations recorded by the source corpus.

We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6af43ea05bf2587ffaae6f53e1899e523a178f0a

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In Statistical and Nonlinear Physics

Citations in the corpus

Finding Statistically Significant Communities in Networks (2010, neutral): “In such cases communities are overlapping (and partitions become covers) and very few methods account for this possibility [18–25], which considerably increases the complexity of the problem.”
Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review (2012, methodology): “• Edge prediction can be performed by comparing the network to an appropriately selectedmodel network, to a similar real world network, or to an ensemble of networks (Liben-Nowell & Kleinberg, 2007; Clauset et al., 2008; Nepusz et al., 2008; Xu et al., 2011a; Gutfraind et al., 2012).”
Scalable Inference of Overlapping Communities (2012, methodology): “In the supplement, we visualized the top authors in the network by a measure of their participation in different communities (bridgeness [17]).”
Efficient discovery of overlapping communities in massive networks (2013, background): “Phys Rev E Stat Nonlin Soft Matter Phys 69(2 Pt 2):026113. 5. Nowicki K, Snijders TAB (2001) Estimation and prediction for stochastic block-”
Controlling edge dynamics in complex networks (2011, methodology): “The other class of networks with the largest difference between the two models is the case of intra-organizational networks [17,23,41].”
Community detection in graphs (2009, methodology): “…by many authors (Danon et al., 2006; Donetti and Muñoz, 2004; Duch and Arenas, 2005; Farkas et al., 2007; Gregory, 2007; Lehmann and Hansen, 2007; Nepusz et al., 2008; Newman, 2004b, 2006a; Noack and Rotta, 2009; Palla et al., 2007, 2005; Pujol et al., 2006; Radicchi et al., 2004; Reichardt and…”
SLPA: Uncovering Overlapping Communities in Social Networks via a Speaker-Listener Interaction Dynamic Process (2011, methodology): “Zhang [10] used the spectral method to embed the graph into k-1 dimensional Euclidean space.”