Centralidade de tempo baseada em conectividade em grafos variantes no tempo

Abstract

Time-varying Graphs (GVTs) allow us to study and better understand the dynamics of real-world systems because they can express the variations of their connections over time. The notion of centrality in GVT scenarios generally refers to metrics that assess the relative importance of nodes over time in the evolution of the complex dynamic network. The notion of the time centrality, which evaluates the relative importance of time instants in dynamic complex networks, is still little explored. Indeed, the few works on the time centrality base their findings on the diffusion process, for example by identifying the best time to receive a message or the crucial time to apply a vaccine in a particular population. In contrast, in this work, we study the Centrality of Time from the point of view of network connectivity. We propose two metrics to identify the most important time in the network. The first is the Time Degree Centrality, which has the traditional idea but calculates the number of connections that each instant of time has. The second, Time PageRank Centrality, classifies the time instants according to the number of incoming edges and the weight loaded by each edge. This follows the principle of traditional PageRank metrics. We model a Public Transport Network through a GVT, in which we evaluate the proposed metrics. In the obtained results we validate that the calculated centralities are effective to identify and classify the most important instants of time of the system. We have also seen that it is fundamental to apply the metrics in the data set that represents the network as a whole because this will identify the most important time instant of the complete network. In the scenario evaluated, we visualize times that stand out each day, such as the number of departures and arrivals.