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Generating hierarchial scale free graphs from fractals

By Julia Komjathy and Karoly Simon

Abstract

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $\Lambda $. 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. Using our (deterministic) fractal $\Lambda $ we generate random graph sequence sharing similar properties.Comment: 4 figure

Topics: Mathematics - Combinatorics, Primary 05C80, Secondary 28A80
Year: 2011
DOI identifier: 10.1016/j.chaos.2011.05.012
OAI identifier: oai:arXiv.org:1104.1024
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