k-Core Organization in Complex Networks

G. J. Baxter (), S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes
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G. J. Baxter: Universidade de Aveiro
S. N. Dorogovtsev: A. F. Ioffe Physico-Technical Institute
A. V. Goltsev: A. F. Ioffe Physico-Technical Institute
J. F. F. Mendes: Universidade de Aveiro

Chapter Chapter 9 in Handbook of Optimization in Complex Networks, 2012, pp 229-252 from Springer

Abstract: Abstract 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.

Keywords: Bootstrap Percolation (BPC); Ordinary Percolation; Cluster Corona; Giant Component; Subcritical Clusters (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0754-6_9

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DOI: 10.1007/978-1-4614-0754-6_9

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