Generating hierarchial scale-free graphs from fractals

Júlia Komjáthy, Károly Simon

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.

Original languageEnglish
Pages (from-to)651-666
Number of pages16
JournalChaos, solitons and fractals
Volume44
Issue number8
DOIs
Publication statusPublished - Aug 1 2011

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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