Fast algorithms for determining (generalized) core groups in social networks

  • Vladimir BatageljEmail author
  • Matjaž Zaveršnik
Regular Article


The structure of a large network (graph) can often be revealed by partitioning it into smaller and possibly more dense sub-networks that are easier to handle. One of such decompositions is based on “k-cores”, proposed in 1983 by Seidman. Together with connectivity components, cores are one among few concepts that provide efficient decompositions of large graphs and networks. In this paper we propose an efficient algorithm for determining the cores decomposition of a given network with complexity \({\mathcal{O}(m)}\), where m is the number of lines (edges or arcs). In the second part of the paper the classical concept of k-core is generalized in a way that uses a vertex property function instead of degree of a vertex. For local monotone vertex property functions the corresponding generalized cores can be determined in \({\mathcal{O}(m\cdot\max(\Delta,\log{n}))}\) time, where n is the number of vertices and Δ is the maximum degree. Finally the proposed algorithms are illustrated by the analysis of a collaboration network in the field of computational geometry.


Core Large network Decomposition Graph algorithm 

Mathematics Subject Classification (2000)

05A18 05C70 05C85 05C90 68R10 68W40 92H30 92G30 93A15 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsFMF, University of LjubljanaLjubljanaSlovenia

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