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，并已在多种场景中得到应用。该度量已被扩展至时间图。时间图中的边带有标签，这些标签反映了节点间交互的时间信息。介数中心性已被推广至时间图设置，而路径的概念也被扩展为时间路径。Bu{\ss}等人及Rymar等人近期的研究表明，时间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)的时间内计算得出，其中T为时间单位数量，m为时间边数，n为节点数。本文改进了先前这些方法的时间复杂度分析，并提出了一种时间复杂度为O(n m T + n^2 T)的算法，用于计算时间图中所有节点的介数中心性。