Generating hierarchial scale free graphs from fractals

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.

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References in corpus (8)

• Emergence of scaling in random networks
• Critical phenomena in complex networks
• Hierarchical Organization in Complex Networks
• The phase transition in inhomogeneous random graphs
• Deterministic Scale-Free Networks
• Graph limits and exchangeable random graphs
• A Geometric Fractal Growth Model for Scale Free Networks
• Multifractal Network Generator

Cited by in corpus (3)

• Analyses of Some Structural Properties on a Class of Hierarchical Scale-free Networks
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