Connectivity-based time centrality in time-varying graphs

Time-varying graphs (TVGs) enable the study and understanding of the dynamics of many real-world networked systems. The notion of centrality in TVG scenarios generally refers to metrics that assess the relative importance of nodes over time in the evolution of a complex dynamic network. In contrast, the notion of Time Centrality, which evaluates the relative importance of time instants in dynamic complex networks, is still little explored. Indeed, the few works on Time Centrality base their findings on the study of diffusion processes, for example, identifying the best time instant to start the dissemination of a message envisaging a more efficient diffusion given the expected network dynamics. In contrast, in this work, we study Time Centrality from a network connectivity perspective. In this context, we propose two connectivity-based metrics to identify the most important time instants in the network. The first metric is the Time Degree Centrality that, analogously to node degree centrality, computes the number of connections that each time instant has. The second metric, Time PageRank Centrality, searches for the time instants that receive the largest number of accumulated connections since they are considered weights at each time instant. To validate the metrics, we model a public multimodal transport network considering time as an aspect of each node. We then apply the proposed metrics and analyse the results from a connectivity-based time centrality perspective. Our results show that the two metrics can identify the most important time instants in different scenarios of complex network dynamics.