Centrality metrics are commonly applied to analyse maritime container service networks, usually modelled as L-graphs (with links representing legs of each service) or P-graphs (with links representing direct port-to-port connections enabled by each service). In fact, maritime container service networks are characterised by routing strategies encompassing multiple alternative routing options between ports – e.g., different sequences of services and/or of transhipment operations in diverse hub ports of call – with an overall transit time depending upon the cumulated frequency of concerned services at loading ports. This resembles exactly the structure of transit networks, modelled usually with a hypergraph-based approach, thus preferable to also represent container service networks. The topology of a hypergraph consists of a dedicated set of links (either in a L- or a P- approach) for each service, and of hyperlinks/waiting links at each port modelling the waiting time as a function of the cumulated frequency of relevant services calling at that port. This allows hypergraphs to account properly for routing strategies in the above sense. Extension of centrality metrics to hypergraphs modelling maritime container services is not straightforward as well and deserves attention. This paper aims to contribute to this topic: theoretical and practical implications of calculation of centrality metrics in hypergraphs are discussed first, by introducing the concepts of HL-graphs and HP-graphs. Then, a new formulation of the betweenness centrality metric consistent with the concept of hyperpath is proposed, leveraging the probability of occurrence of each elemental path in an hyperpath. Finally, an application to a worldwide network of container services related to year 2019 showcases the effectiveness and the easiness of calculation of the new proposed betweenness centrality metric.

中心性指标通常用于分析海运集装箱服务网络，通常建模为 L 图（链接表示每个服务的支线）或 P 图（链接表示每个服务启用的直接端口到端口连接）。事实上，海运集装箱服务网络的特点是路由策略包含港口之间的多种替代路由选择——例如，不同的停靠枢纽港的不同服务序列和/或转运操作——总的运输时间取决于累计频率有关装货港的服务。这与运输网络的结构完全相似，通常使用基于超图的方法建模，因此更适合表示容器服务网络。超图的拓扑结构由每个服务的一组专用链接（L-或 P-方法）和每个端口的超链接/等待链接组成，将等待时间建模为相关的累积频率的函数。在该端口调用的服务。这允许超图正确考虑上述意义上的路由策略。将中心性度量扩展到对海运集装箱服务建模的超图也并不简单，值得关注。本文旨在为该主题做出贡献：首先通过介绍 HL-graphs 和 HP-graphs 的概念讨论超图中中心性度量计算的理论和实践意义。然后，提出了与超路径概念一致的介数中心性度量的新公式，利用超路径中每个元素路径的发生概率。最后，与 2019 年相关的全球容器服务网络的应用程序展示了新提议的中介中心性度量的有效性和计算的简便性。