High dimensional random Apollonian networks

TL;DR

This paper introduces high dimensional random Apollonian networks, a new network model with small-world and scale-free properties, supported by analytical and simulation results.

Contribution

It presents a simple algorithm for generating high dimensional Apollonian networks and derives their degree distribution, clustering, and path length analytically.

Findings

Degree distributions match simulations and real networks

Clustering coefficients depend on network dimension

Average path length grows logarithmically with network size

Abstract

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We prove also analitically that the average path length of the networks increases at most logarithmically with the number of vertices.