Generating hierarchial scale-free graphs from fractals

Júlia Komjáthy, K. Simon

Research output: Contribution to journalArticle

13 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 2011

Fingerprint

Fractal
Graph in graph theory
Scale-free Networks
Degree Distribution
Random Graphs
Logarithm
Directed Graph
Network Model
Power Law
Sharing
Exponent
Clustering
Verify
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Generating hierarchial scale-free graphs from fractals. / Komjáthy, Júlia; Simon, K.

In: Chaos, Solitons and Fractals, Vol. 44, No. 8, 08.2011, p. 651-666.

Research output: Contribution to journalArticle

Komjáthy, Júlia ; Simon, K. / Generating hierarchial scale-free graphs from fractals. In: Chaos, Solitons and Fractals. 2011 ; Vol. 44, No. 8. pp. 651-666.
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