A new general family of deterministic hierarchical networks

TL;DR

This paper introduces a new deterministic hierarchical network family that generalizes existing models, enabling better analysis of their properties and efficient computation of shortest paths in complex systems.

Contribution

A novel deterministic hierarchical network family is proposed, generalizing previous models and allowing precise analysis of key network parameters and efficient path algorithms.

Findings

Networks exhibit small-world and scale-free properties.

Characterized diameter and radius of the networks.

Proposed an efficient shortest-path algorithm.

Abstract

It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and the diameter. Moreover, as a by product, an efficient shortest-path local algorithm is proposed.