Hypergraph-based centrality metrics for maritime container service networks: A worldwide application

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.