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 ¿. 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 ¿ we generate random graph sequence sharing similar properties.
Original language | English |
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Pages (from-to) | 651-666 |
Number of pages | 16 |
Journal | Chaos, Solitons and Fractals |
Volume | 44 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2011 |