Com_Modularity - Modularity and community structure in...

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Modularity and community structure in networks M. E. J. Newman* Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109 Edited by Brian Skyrms, University of California, Irvine, CA, and approved April 19, 2006 (received for review February 26, 2006) Many networks of interest in the sciences, including social net- works, computer networks, and metabolic and regulatory net- works, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community struc- ture is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as ‘‘modularity’’ over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the net- work, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets. clustering u partitioning u modules u metabolic network u social network M any systems of scientific interest can be represented as networks, sets of nodes or vertices joined in pairs by lines or edges. Examples include the internet and the worldwide web, metabolic networks, food webs, neural networks, communica- tion and distribution networks, and social networks. The study of networked systems has a history stretching back several centu- ries, but it has experienced a particular surge of interest in the last decade, especially in the mathematical sciences, partly as a result of the increasing availability of accurate large-scale data describing the topology of networks in the real world. Statistical analyses of these data have revealed some unexpected structural features, such as high network transitivity (1), power-law degree distributions (2), and the existence of repeated local motifs (3); see refs. 4–6 for reviews. One issue that has received a considerable amount of attention is the detection and characterization of community structure in networks (7, 8), meaning the appearance of densely connected groups of vertices, with only sparser connections between groups (Fig. 1). The ability to detect such groups could be of significant practical importance. For instance, groups within the worldwide web might correspond to sets of web pages on related topics (9); groups within social networks might correspond to social units or communities (10). Merely the finding that a network contains tightly knit groups at all can convey useful information: if a metabolic network were divided into such groups, for instance, it could provide evidence for a modular view of the network’s dynamics, with different groups of nodes performing different functions with some degree of independence (11, 12). Past work on methods for discovering groups in networks
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This note was uploaded on 05/20/2011 for the course CAP 5515 taught by Professor Ungor during the Spring '08 term at University of Florida.

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Com_Modularity - Modularity and community structure in...

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