Deterministic hierarchical networks

TL;DR

This paper introduces a deterministic approach to analyze hierarchical small-world scale-free networks, providing exact calculations of key network parameters to better understand complex systems.

Contribution

It presents a method for exactly determining parameters of deterministic hierarchical networks, complementing stochastic models.

Findings

Calculated radius, diameter, clustering coefficient, and degree distribution for the network family.

Demonstrated the applicability of the deterministic method to real-world complex systems.

Enhanced understanding of network structure through exact parameter determination.

Abstract

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the systems modeled. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.