Finding community structure in networks using the eigenvectors of matrices

作者：M. E. J. Newman · 发表于：Physical Review E · 年份：2006 · DOI：10.1103/physreve.74.036104 · 被引用次数：4918 · 研究领域：Complex Network Analysis Techniques、Graph theory and applications、Opinion Dynamics and Social Influence

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 centrality measure that identifies 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.