Simplex triangulation induced scale-free networks

Details Simplex triangulation induced scale-free networks Simplex triangulation induced scale-free networks

2005-05-07

arxiv.org/abs/cond-mat/0505175v1

Dynamics of Continuous, Discrete and Impulsive Systems B 13, 505-510 (2006)

Physics

Condensed Matter

Statistical Mechanics

6 pages, no figures

Scientific paper

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.

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