High Dimensional Apollonian Networks

TL;DR

This paper introduces a straightforward algorithm for generating high-dimensional Apollonian networks that exhibit small-world and scale-free properties, with analytical formulas derived for key network metrics.

Contribution

The paper presents a novel algorithm for constructing high-dimensional Apollonian networks and provides analytical expressions for their degree distribution, clustering coefficient, and diameter.

Findings

Networks display small-world and scale-free characteristics.

Analytical formulas for degree distribution, clustering coefficient, and diameter are derived.

Network properties are determined by their dimension.

Abstract

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension.