Simplex triangulation induced scale-free networks

Abstract

We propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called simplex triangulation networks(STNs) as they can be considered as a kind of network representation of simplex triangulation. We obtain the analytic results of power-law exponent $\gamma =2+\frac{1}{d-1}$ for $d$-dimensional STNs, and clustering coefficient $C$. We prove that the increasing tendency of average distance of STNs is a little slower than the logarithm of the number of nodes in STNs. In addition, the STNs possess hierarchical structure as $C(k)\sim k^{-1}$ when $k\gg d$ that in accord with the observations of many real-life networks.

6 pages, no figures

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• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
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• Connectivity of Growing Random Networks
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• Maximal planar networks with large clustering coefficient and power-law degree distribution

Cited by in corpus (2)

• Exploring complex networks via topological embedding on surfaces
• Complex Network Properties of Chinese Natural Science Basic Research