The Multiplex Efficiency Index: unveiling the Brazilian Air Transportation Multiplex Network -- BATMN

TL;DR

This paper introduces the Multiplex Efficiency Index to quantify the evolving connectivity diversity of multiplex networks, demonstrated through the analysis of Brazil's air transportation system over time.

Contribution

The paper presents a novel index for measuring multiplex network efficiency that accounts for layer variations and temporal changes, applied to Brazil's air transportation network.

Findings

The index effectively captures fluctuations in network efficiency.

It remains unbiased despite changes in the number of layers.

Applied to Brazil, it reveals impacts of privatization and mergers.

Abstract

Modern society is increasingly massively connected, reflecting an omnipresent tendency to organize social, economic, and technological structures in complex networks. Recently, with the advent of the so-called multiplex networks, new concepts and tools were necessary to better understand the characteristics of this type of system, as well as to analyze and quantify its performance and efficiency. The concept of diversity in multiplex networks is a striking example of this intrinsically interdisciplinary efort to better understand the nature of complex networks. In this work, we introduce the Multiplex Efficiency Index, which allows quantifying the temporal evolution of connectivity diversity, particularly when the number of layers of the multiplex network varies over time. Using data related to air passenger transportation in Brazil we investigate, through the new index, how the Brazilian air transportation network has being changing over the years due to the privatization processes of airports and mergers of airlines in Brazil. Besides that, we show how the Multiplex Efficiency Index is able to quantify fluctuations in network efficiency in a non-biased way, limiting its values between 0 and 1, taking into account the number of layers in the multiplex structure. We believe that the proposed index is of great value for the evaluation of the performance of any multiplex network, and to analyze, in a quantitative way, its temporal evolution independently of the variation in the number of layers.