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K-core Decomposition


Definition

The k-core of graph is a maximal subgraph in which each vertex has at least degree k. The coreness of a vertex is k if it belongs to the k-core but not to the (k+1)-core.

K-shell decomposition to directed networks
V. Batagelj, M. Zaversnik, Generalized cores, 2002, arXiv:cs.DS/0202039.

K-shell decomposition to weighted networks
A. Garas, F. Schweitzer, S. Havlin, A k-shell decomposition method for weighted networks, New J. Phys. 14 (2012) 083030.

References

  • BATAGELJ, V. & ZAVERSNIK, M. 2003. An O (m) algorithm for cores decomposition of networks. arXiv preprint cs/0310049. Publisher web site Endnote RIS file
  • CSARDI, G. & NEPUSZ, T. 2006. The igraph software package for complex network research. InterJournal, Complex Systems, 1695. [http://igraph.org]
  • SEIDMAN, S. B. 1983. Network structure and minimum degree. Social Networks, 5, 269-287. DOI: 10.1016/0378-8733(83)90028-X Publisher web site Endnote RIS file


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