Quantifying hierarchy in public transport networks: Developing a new metric

Abstract

Due to increasing pressure on the system, the functioning of public transport networks (PTN) in metropolitan areas is crucial for future mobility. Within these networks, hierarchical levels can be distinguished where different levels have different functions. These hierarchical levels can be analyzed but there is no way to quantitatively determine the hierarchy in a PTN. Therefore, this paper presents a metric to quantify the hierarchy in PTN to increase the understanding of these complex networks. In order to determine the hierarchy, a metric is developed based on a combined topological and empirical approach. The metric is a multiplication of three different elements which are the topological influence, (non-)redundancy and transfer potential. Together these elements are applied to define the hierarchical degree of nodes in a network. Furthermore, to determine the hierarchy of a network as a whole, a hierarchical coefficient, based on the distribution and inequality of the hierarchical degree in the network is developed. The metric has been applied to case-studies for the Dutch cities of Amsterdam and Rotterdam which allows for different state and cross-network comparison. The results show some expected yet non-trivial results identifying different patterns in network structures for network states and different spatial distribution of hierarchy between networks. Furthermore, by dividing the network into functional levels, a hierarchical structure can be identified.
Throughout this study, a new method to quantify hierarchy in PTN, based on different approaches, is developed which can be seen as the most important contribution of this research. While this study explores the implications of this metric, it can be applied in numerous different contexts. Furthermore, in potential the metric has numerous network related applications such decreasing vulnerability and solving bottlenecks.