Temporal Betweenness Centrality on Shortest Paths

Betweenness centrality measure assesses the importance of nodes in a graph and has been used in a variety of contexts. Betweenness centrality has also been extended to temporal graphs. Temporal graphs have edges that bear labels according to the time of the interactions between the nodes. Betweenness centrality has been extended to the temporal graph settings, and the notion of paths has been extended to temporal paths. Recent results by Bu{\ss} et al. and Rymar et al. showed that the betweenness centrality of all nodes in a temporal graph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of time units, m the number of temporal edges and n the number of nodes. In this paper, we improve the running time analysis of these previous approaches to compute the betweenness centrality of all nodes in a temporal graph. We give an algorithm that runs in O(n m T + n^2 T ).