{"_id":"aakqPdAX3RFk5BAEg","bibbaseid":"newman-findingcommunitystructureinnetworksusingtheeigenvectorsofmatrices","authorIDs":[],"author_short":["Newman, M. E J"],"bibdata":{"bibtype":"article","type":"article","title":"Finding Community Structure in Networks Using the Eigenvectors of Matrices","volume":"74","issn":"15393755","doi":"10.1103/PhysRevE.74.036104","abstract":"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.","number":"3","journaltitle":"Physical Review E - Statistical, Nonlinear, and Soft Matter Physics","date":"2006","author":[{"propositions":[],"lastnames":["Newman"],"firstnames":["M.","E","J"],"suffixes":[]}],"file":"/home/dimitri/Nextcloud/Zotero/storage/TJLPZTK4/Newman - 2006 - Finding community structure in networks using the eigenvectors of matrices.pdf","eprinttype":"pmid","eprint":"17025705","bibtex":"@article{newmanFindingCommunityStructure2006,\n title = {Finding Community Structure in Networks Using the Eigenvectors of Matrices},\n volume = {74},\n issn = {15393755},\n doi = {10.1103/PhysRevE.74.036104},\n abstract = {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.},\n number = {3},\n journaltitle = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n date = {2006},\n author = {Newman, M. E J},\n file = {/home/dimitri/Nextcloud/Zotero/storage/TJLPZTK4/Newman - 2006 - Finding community structure in networks using the eigenvectors of matrices.pdf},\n eprinttype = {pmid},\n eprint = {17025705}\n}\n\n","author_short":["Newman, M. E J"],"key":"newmanFindingCommunityStructure2006","id":"newmanFindingCommunityStructure2006","bibbaseid":"newman-findingcommunitystructureinnetworksusingtheeigenvectorsofmatrices","role":"author","urls":{},"downloads":0},"bibtype":"article","biburl":"https://raw.githubusercontent.com/dlozeve/newblog/master/bib/all.bib","creationDate":"2020-01-08T20:39:39.045Z","downloads":0,"keywords":[],"search_terms":["finding","community","structure","networks","using","eigenvectors","matrices","newman"],"title":"Finding Community Structure in Networks Using the Eigenvectors of Matrices","year":null,"dataSources":["3XqdvqRE7zuX4cm8m"]}