Quantification and comparison of hierarchy in Public Transport Networks

Network hierarchy describes the relative arrangement of network elements and reflects its fun-damental structure. We propose a multi-dimensional topology-based method for quantifying and comparing the extent to which different Public Transport Networks (PTNs) exhibit a hierarchical structure. The proposed method considers the uneven distribution of node importance with different definitions (e.g., degree centrality and betweenness centrality) in a PTN, the clustering of nodes and the node connection patterns. We apply the developed method on 63 high-capacity PTNs worldwide using General Transit Feed Specification (GTFS) data. In addition to global indicators, we use the goodness-of-fit between the probability density function of local indicators and a skew-normal distribution to quantify the extent of PTN hierarchy. Results show that the scale-free network structure and preferential attachment do not vary much across PTNs. In contrast, stop accessibility and traffic intermediacy vary considerably across PTNs as reflected by the closeness centrality and betweenness centrality distributions. Lastly, metro systems exhibit a more hierarchical structure than their tram and Bus Rapid Transit (BRT) counterparts. This work makes a first step towards a better mapping and comparison of different PTNs, which can assist academics and practitioners in better (re)designing and planning the PTNs of the future.