Finding Community Structure in Networks Using the Eigenvectors of Matrices. Newman, M. E J
doi  abstract   bibtex   
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.
@article{newmanFindingCommunityStructure2006,
  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 = {Newman, M. E J},
  file = {/home/dimitri/Nextcloud/Zotero/storage/TJLPZTK4/Newman - 2006 - Finding community structure in networks using the eigenvectors of matrices.pdf},
  eprinttype = {pmid},
  eprint = {17025705}
}
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