Generating hierarchial scale-free graphs from fractals

Júlia Komjáthy and Károly Simon

Chaos, Solitons & Fractals, 2011, vol. 44, issue 8, 651-666

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:8:p:651-666

DOI: 10.1016/j.chaos.2011.05.012

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