Diamond Hierarchical Network with Discrete, Unrelated, Self-Similar and Fractal Feature

Abstract

In this paper, a deterministic network called diamond hierarchical network (DHN) is first introduced. The topological properties of the network such as degree distribution, clustering coefficient, average path length and degree correlation are calculated analytically. The scaling of the average path length is the exponential growth of the total number of network nodes, the network does not have the nature of small-world. A small-world diamond hierarchical network (SWDHN) is defined according to the diamond hierarchical network, some basic properties of the network are studied, and the small-world phenomenon of SWDHN arises. Box dimension and fractality of DHN and SWDHN are considered.