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Finding community structure in networks using the eigenvectors of matrices (2006)
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@MISC{Newman06findingcommunity,
author = {M. E. J. Newman},
title = {Finding community structure in networks using the eigenvectors of matrices },
year = {2006}
}
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Abstract
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.
Keyphrases
finding community structure bipartite structure possible division benefit function central position community detection real-world complex network maximization process modularity matrix robust approach previous work graph laplacian new centrality measure spectral measure several result graph partitioning calculation possible algorithm higher-than-average density community structure
