Parallel Random Apollonian Networks

TL;DR

This paper introduces a simple algorithm for generating growing Parallel Random Apollonian Networks in any dimension, demonstrating their small-world and scale-free properties through analytical and simulation results.

Contribution

The paper presents a novel algorithm for P-RAN, introduces new structural parameters, and provides analytical formulas for key network metrics.

Findings

P-RAN networks exhibit small-world properties.

Degree and clustering coefficients are analytically derived.

Simulation results agree with theoretical predictions.

Abstract

We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of P-RAN, we introduce new parameters that we refer to as the parallel degree and the parallel coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network. We provide analytical derivations for the computation of the degree and parallel degree distributions, parallel and clustering coefficients. We give an upper bound for the average path lengths for P-RAN and finally show that our derivations are in very good agreement with our simulations.