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Modern society is increasingly massively connected, reflecting an omnipresenttendency to organize social, economic, and technological structures in complexnetworks. Recently, with the advent of the so-called multiplex networks, newconcepts and tools were necessary to better understand the characteristics ofthis type of system, as well as to analyze and quantify its performance andefficiency. The concept of diversity in multiplex networks is a strikingexample of this intrinsically interdisciplinary efort to better understand thenature of complex networks. In this work, we introduce the Multiplex EfficiencyIndex, which allows quantifying the temporal evolution of connectivitydiversity, particularly when the number of layers of the multiplex networkvaries over time. Using data related to air passenger transportation in Brazilwe investigate, through the new index, how the Brazilian air transportationnetwork has being changing over the years due to the privatization processes ofairports and mergers of airlines in Brazil. Besides that, we show how theMultiplex Efficiency Index is able to quantify fluctuations in networkefficiency in a non-biased way, limiting its values between 0 and 1, takinginto account the number of layers in the multiplex structure. We believe thatthe proposed index is of great value for the evaluation of the performance ofany multiplex network, and to analyze, in a quantitative way, its temporalevolution independently of the variation in the number of layers.

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