Modularity and community structure in networks

@misc{citeulike:686555, abstract = {Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.}, author = {Newman, M. E. J. }, citeulike-article-id = {686555}, comment = {Provides method for clustering graphs, including membership strength. "A good division of a network into communities is not merely one in which there are few edges between communities; it is one in which there are fewer than expected edges between communities" "we comput the leading eigenvector of the modularity matrix and divide the vertices into two groups according to the signs of the elements in this vector" "A network is indivisible if the modularity matrix has no positive eigenvalues" Provides a fast implementation based on power method.}, eprint = {physics/0602124}, keywords = {clustering, math, web-graph}, month = {Feb}, posted-at = {2008-05-02 16:08:43}, priority = {0}, title = {Modularity and community structure in networks}, url = {http://arxiv.org/abs/physics/0602124}, year = {2006} }

TY - ELEC ID - citeulike:686555 L3 - citeulike-article-id:686555 TI - Modularity and community structure in networks N2 - Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets. KW - clustering KW - math KW - web-graph N1 - Provides method for clustering graphs, including membership strength. "A good division of a network into communities is not merely one in which there are few edges between communities; it is one in which there are fewer than expected edges between communities" "we comput the leading eigenvector of the modularity matrix and divide the vertices into two groups according to the signs of the elements in this vector" "A network is indivisible if the modularity matrix has no positive eigenvalues" Provides a fast implementation based on power method. AU - Newman, MEJ PY - 2006/Feb/17/ UR - http://arxiv.org/abs/physics/0602124 ER -