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 ).

翻译：介数中心性度量用于评估图中节点的重要性，并被广泛应用于多种场景。该度量已被扩展至时序图。时序图的边带有标签，标识节点间交互发生的时间。介数中心性已被扩展到时序图设置，路径概念也被扩展为时序路径。Bu{\ss}等人和Rymar等人近期研究表明，时序图中所有节点的介数中心性可在O(n^3 T^2)或O(n^2 m T^2)时间内计算，其中T为时间单位数，m为时序边数，n为节点数。本文改进了先前方法在计算时序图所有节点介数中心性时的运行时间分析，提出了一种运行时间为O(n m T + n^2 T)的算法。