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 effort 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.
Highlights
Efficiency, according to the Cambridge Dictionary is “the condition or fact of producing the results you want without waste, or a particular way in which this is done” or, by Oxford, “the quality of doing something well with no waste of time or money”
In this sense, supported by the definition of diversity of a multiplex network introduced in a recent w ork[6], we present the Multiplex Efficiency Index (E -index), which is a modified version of the diversity measure capable of quantifying the connectivity patterns of a multiplex network on a normalized scale from 0 to 1, which is independent of the number of layers
Combining the E-index and diversity ordering, we have found a way of analyzing the efficiency of multiplex network, regardless of the number of layers
Summary
Efficiency, according to the Cambridge Dictionary is “the condition or fact of producing the results you want without waste, or a particular way in which this is done” or, by Oxford, “the quality of doing something well with no waste of time or money”. A greater diversification implies in the presence of less overlapping links between layers, reducing the redundancy of the connections, and expanding the possibilities of using different paths to explore the structure in a more efficient way In this sense, supported by the definition of diversity of a multiplex network introduced in a recent w ork[6], we present the Multiplex Efficiency Index (E -index), which is a modified version of the diversity measure capable of quantifying the connectivity patterns of a multiplex network on a normalized scale from 0 to 1, which is independent of the number of layers. To quantify connection differences in social n etworks[7], showing user sets that have similar or distinct connections, to analyze networks of criminal relationships[8], to point out similarities (or differences) between the preferences of a group of people or to verify the protein interactions of the human HIV-1 v irus[6], to check the supply of transportation modalities for a given r egion[9], among many others
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
