Time Centrality in Dynamic Complex Networks

There is an ever-increasing interest in investigating dynamics in timevarying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. In this paper, we thus introduce and investigate the notion of time centrality in TVGs. Analogously to node centrality, time centrality evaluates the relative importance of time instants in dynamic complex networks. In this context, we present two time centrality metrics related to diffusion processes. We evaluate the two defined metrics using both a real-world dataset representing an in-person contact dynamic network and a synthetically generated randomized TVG. We validate the concept of time centrality showing that diffusion starting at the best classified time instants (i.e. the most central ones), according to our metrics, can perform a faster and more efficient diffusion process. 1 ar X iv :1 50 4. 00 24 1v 3 [ cs .S I] 6 S ep 2 01 5