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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
ScopusOSTI

C%2B%2B tensor toolbox user manual

Plantenga, Todd P.; Kolda, Tamara G.

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

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TYPE SAND Report YEAR 2012
OSTIDOI
Results 101–125 of 199
Results 101–125 of 199