Generating hierarchial scale free graphs from fractals

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 $Λ$. 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. Using our (deterministic) fractal $Λ$ we generate random graph sequence sharing similar properties.

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