High-speed rail (HSR) is frequently seen as a promising alternative for long-distance travel by air and road, given its environmental advantages whilst offering a competitive level of service. However, a European HSR-network is yet to be realised, with the current state amounting to a patchwork of poorly connected subnetworks. Consequently, this results in a suboptimal performance from a user, operator and societal perspective. We present a customised version of the Transit Network Design and Frequency Setting Problem (TNDFSP) for the long-distance transport context and HSR in particular. We apply an adapted version of a heuristic solution approach to analyse the users’, operators’ and societal performance of a European HSR-network by conducting an extensive series of experiments to test the network's performance under various policy priorities and HSR design variables. Our experiment results show that designs resulting from the consideration of externalities yield more extensive networks with larger coverage and modal shifts. For such networks to materialise, high public investments are needed. The obtained network designs contain four different line types, exhibit spatial disparities in network density, and allow for the identification of potential hubs and critical infrastructure. The strong network integration with overlapping and border-crossing lines of substantial lengths highlights the importance of cross-border cooperation and rail interoperability. We hope our findings will contribute to the ongoing public and professional debates on designing an attractive and competitive European HSR-network.

Public transport networks constitute critical infrastructure in urban systems. Public transport networks are characterised by their hierarchical structure, yet methods to quantify their underlying hierarchy are lacking. We propose a metric for quantifying the hierarchy in public transport networks which incorporates topological as well as passenger flow information. Our proposed metric consists of three components which jointly define the relative hierarchical position of nodes across the network while the distribution of hierarchy defines the hierarchy of the network itself. We apply the metric to the case studies of Amsterdam and Rotterdam to demonstrate its usefulness in comparing different network states both within and across networks. Using this metric, we identify different patterns in network structures for network states and different spatial distributions of hierarchy between networks. Furthermore, by dividing the network into functional levels, we identify a multilayer hierarchical structure that describes the functionality of the network. The potential application of this metric relates to the assessment of network development scenarios, evaluating bottlenecks and analysing the network vulnerability. Furthermore, the metric is potentially suitable for assessing different network structures such as aviation or maritime networks.