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Community structure and scale-free collections of Erdos-Rényi graphs

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Seshadhri, C.; Kolda, Tamara G.; Pinar, Ali P.

Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models. We formally define a community to be a subgraph that is internally highly connected and has no deeper substructure. We use tools of combinatorics to show that any such community must contain a dense Erdos-Rényi (ER) subgraph. Based on mathematical arguments, we hypothesize that any graph with a heavy-tailed degree distribution and community structure must contain a scale-free collection of dense ER subgraphs. These theoretical observations corroborate well with empirical evidence. From this, we propose the Block Two-Level Erdos-Rényi (BTER) model, and demonstrate that it accurately captures the observable properties of many real-world social networks. © 2012 American Physical Society.

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TYPE Conference YEAR 2012
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Latent clustering on graphs with multiple edge types

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Rocklin, Matthew; Pinar, Ali P.

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics, and so allowing graphs with multivariate edges significantly increases modeling power. In this context the clustering problem becomes more challenging. Each edge/metric provides only partial information about the data; recovering full information requires aggregation of all the similarity metrics. We generalize the concept of clustering in single-edge graphs to multi-edged graphs and discuss how this generates a space of clusterings. We describe a meta-clustering structure on this space and propose methods to compactly represent the meta-clustering structure. Experimental results on real and synthetic data are presented. © 2011 Springer-Verlag.

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TYPE Conference YEAR 2011
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Results 126–150 of 172
Results 126–150 of 172