Flux of information in scale-free networks

TL;DR

This paper explores how information spreads in scale-free networks, demonstrating that the dynamics follow q-exponential functions and are best described by Tsallis Statistics, with implications for understanding complex systems.

Contribution

It introduces a mechanism based on local information spread in scale-free networks and shows that the dynamics follow q-exponential behavior, linking to Tsallis Statistics.

Findings

Information spread follows q-exponential functions.

Tsallis Statistics effectively describe the dynamics.

Parameter behavior analyzed as network size increases.

Abstract

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network's properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks. Here we discuss a mechanism based on how information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.