Information Super-Diffusion on Structured Networks

TL;DR

This study investigates how network topology influences information diffusion, revealing universal power-law behaviors and super-diffusive dynamics, and emphasizes the importance of matching transport rules with network structure for optimal efficiency.

Contribution

It introduces a model analyzing information packet diffusion on structured networks, highlighting the universal impact of topology and the effects of different local transport rules.

Findings

Power-law distributions in transit times and velocities.

Super-diffusive behavior confirmed by multifractal analysis.

Network topology critically affects transport efficiency.

Abstract

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by power-laws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.