k-Core Organization in Complex Networks

  • G. J. Baxter
  • S. N. Dorogovtsev
  • A. V. Goltsev
  • J. F. F. Mendes
Part of the Springer Optimization and Its Applications book series (SOIA, volume 57)


We analyse the complex network architectures based on the k-core notion, where the k-core is the maximal subgraph in a network, whose vertices all have internal degree at least k. We explain the nature of the unusual “hybrid” phase transition of the emergence of a giant k-core in a network, which combines a jump in the order parameter and a critical singularity, and relate this transition to critical phenomena in other systems. Finally, we indicate generic features and differences between the k-core problem and bootstrap percolation.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • G. J. Baxter
    • 1
  • S. N. Dorogovtsev
    • 2
  • A. V. Goltsev
    • 2
  • J. F. F. Mendes
    • 1
  1. 1.Departamento de Física, I3NUniversidade de AveiroAveiroPortugal
  2. 2.A. F. Ioffe Physico-Technical InstituteSt. PetersburgRussia

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