The notions of betweenness centrality (BC) and group betweenness centrality (GBC) are widely used in social network analyses. We introduce variants of them; namely, the k-step BC and k-step GBC. The k-step GBC of a group of vertices in a network is a measure of the likelihood that at least one group member will get the information communicated between pairs of vertices through shortest paths within the first k steps of the start of the communication. The k-step GBC of a single vertex is the k-step BC of that vertex. The introduced centrality measures may find uses in applications where it is important or critical to obtain the information within a fixed time of the start of the communication. For the introduced centrality measures, we propose an algorithm that can compute successively the k-step GBC of several groups of vertices. The performance of the proposed algorithm is evaluated through computational experiments. The use of the new BC measures leads to an earlier control of the information (virus, malware, or rumor) before it spreads through the network.

中文翻译：

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k步中间性

中间性中心（BC）和群体中间性中心（GBC）的概念被广泛用于社交网络分析中。我们介绍它们的变体。即，k步BC和k步GBC。网络中一组顶点的k步GBC是对至少一个组成员将通过前k个最短路径获得成对顶点之间的信息的可能性的度量开始通信的步骤。单个顶点的k步GBC是该顶点的k步BC。所引入的集中度度量可以在对于在通信开始的固定时间内获取信息很重要或至关重要的应用中找到用处。对于引入的中心度度量，我们提出了一种可以连续计算几组顶点的k步GBC的算法。通过计算实验评估了该算法的性能。使用新的BC措施可以使信息（病毒，恶意软件或谣言）在通过网络传播之前得到更早的控制。