Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

Finding community structure in networks using the eigenvectors of matrices

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.Comment: 22 pages, 8 figures, minor corrections in this versio

Attributed Networks Partitioning Based on Modularity Optimization

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