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

Abstract

Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional hierarchical networks. Secondly, we study the precise results of some structural properties to derive small-world effect and scale-free feature. Thirdly, it is found that the constructed network is sparse through the average degree and density. Fourthly, it is also demonstrated the degree distributions of hub nodes and the bottom nodes are the power law and exponential, respectively. Finally, we prove that clustering coefficient with a definite value z tends to stabilize at a lower bound as t iterates to a certain number, and the average distance of G_{t}^{z} has a increasing relationship along with the value of lnN_{t}.

References in corpus (4)

• The clustering coefficient and community structure of bipartite networks
• Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation
• Average distance in a hierarchical scale-free network: an exact solution
• Counterexample: scale-free networked graphs with invariable diameter and density feature