Quantifying the hierarchy of public transport networks

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 multi-layer 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.