Deterministic scale-free networks created in a recursive manner

TL;DR

This paper introduces a family of deterministic scale-free networks constructed recursively, with adjustable degree exponents, small-world properties, and exact calculations of key network metrics.

Contribution

It presents a novel recursive method to create deterministic scale-free networks with tunable parameters and exact analytical results for their structural properties.

Findings

Degree exponent can be tuned by parameters

Clustering coefficient inversely proportional to degree

Diameter grows logarithmically with network size

Abstract

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering coefficient and the diameter. The major points of our results indicate: the degree exponent can be adjusted; the clustering coefficient of each individual vertex is inversely proportional to its degree and the average clustering coefficient of all vertices approaches to a nonzero value in the infinite network order; and the diameter grows logarithmically with the number of network vertices.