Simplex Triangulation Induced Scale-free Networks

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 γ = 2 + 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) ∼ k when k ≫ d that in accord with the observations of many real-life networks.