On a geometrization of the Chung–Lu model for complex networks

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13 Citations (Scopus)


We consider a model for complex networks that was introduced by Krioukov et al. (2010, Phys. Rev. E, 82, 036106), where the intrinsic hierarchies of a network are mapped into the hyperbolic plane. Krioukov et al. show that this model exhibits clustering and the distribution of its degrees has a power-law tail. We show that asymptotically this model locally behaves like the well-known Chung–Lu model in which two nodes are joined independently with probability proportional to the product of some pre-assigned weights whose distribution follows a power law. Using this, we further determine exactly the asymptotic distribution of the degree of an arbitrary vertex.

Original languageEnglish
Number of pages27
JournalJournal of Complex Networks
Early online date6 Jan 2015
Publication statusPublished - 6 Jan 2015


  • Mathematical analysis of networks


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