Generating hierarchial scale free graphs from fractals

Details Generating hierarchial scale free graphs from fractals Generating hierarchial scale free graphs from fractals

2011-04-06

arxiv.org/abs/1104.1024v1

Mathematics

Combinatorics

4 figures

Scientific paper

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.

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