2006/05/31 by M. E. J. Newman · 3 citations
Physics and Astronomy · #cond-mat.stat-mech #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1103/physreve.74.036104
published as Phys. Rev. E 74, 036104 (2006) · 22 pages, 8 figures, minor corrections in this version
arxiv created 2006/07/23 · arxiv updated 2009/12/01
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.