  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.
