dorsal/arxiv
View SchemaFinding community structure in networks using the eigenvectors of matrices
| Authors | M. E. J. Newman |
|---|---|
| Categories | |
| ArXiv ID | physics/0605087 |
| URL | https://arxiv.org/abs/physics/0605087 |
| DOI | 10.1103/PhysRevE.74.036104 |
| Journal | Phys. Rev. E 74, 036104 (2006) |
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 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.
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"abstract": "We consider the problem of detecting communities or modules in networks,\ngroups of vertices with a higher-than-average density of edges connecting them.\nPrevious work indicates that a robust approach to this problem is the\nmaximization of the benefit function known as \"modularity\" over possible\ndivisions of a network. Here we show that this maximization process can be\nwritten in terms of the eigenspectrum of a matrix we call the modularity\nmatrix, which plays a role in community detection similar to that played by the\ngraph Laplacian in graph partitioning calculations. This result leads us to a\nnumber of possible algorithms for detecting community structure, as well as\nseveral other results, including a spectral measure of bipartite structure in\nnetworks and a new centrality measure that identifies those vertices that\noccupy central positions within the communities to which they belong. The\nalgorithms and measures proposed are illustrated with applications to a variety\nof real-world complex networks.",
"arxiv_id": "physics/0605087",
"authors": [
"M. E. J. Newman"
],
"categories": [
"physics.data-an",
"cond-mat.stat-mech",
"physics.soc-ph"
],
"doi": "10.1103/PhysRevE.74.036104",
"journal_ref": "Phys. Rev. E 74, 036104 (2006)",
"title": "Finding community structure in networks using the eigenvectors of matrices",
"url": "https://arxiv.org/abs/physics/0605087"
},
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