Orientations and matrix function-based centralities in multiplex network analysis of urban public transport

TL;DR

This paper analyzes urban public transport networks using multiplex network models, compares their orientations with street networks across European cities, and explores matrix function-based centrality measures to gain insights into urban system geometry.

Contribution

It introduces a multiplex network framework for urban transport analysis and applies matrix function-based centralities, providing new tools for understanding urban spatial structures.

Findings

German transport networks are mainly east-west oriented.

Most public transport networks lack a distinct north-south orientation.

Matrix function-based centralities reveal detailed geometrical properties of urban systems.

Abstract

We study urban public transport systems by means of multiplex networks in which stops are represented as nodes and each line is represented by a layer. We determine and visualize public transport network orientations and compare them with street network orientations of the $36$ largest German as well as $18$ selected major European cities. We find that German urban public transport networks are mainly oriented in a direction close to the cardinal east-west axis, which usually coincides with one of two orthogonal preferential directions of the corresponding street network. While this behavior is present in only a subset of the considered European cities it remains true that none but one considered public transport network has a distinct north-south-like preferential orientation. Furthermore, we study the applicability of the class of matrix function-based centrality measures, which has recently been generalized from single-layer networks to layer-coupled multiplex networks, to our more general urban multiplex framework. Numerical experiments based on highly efficient and scalable methods from numerical linear algebra show promising results, which are in line with previous studies. The centrality measures allow detailed insights into geometrical properties of urban systems such as the spatial distribution of major transport axes, which can not be inferred from orientation plots. We comment on advantages over existing methodology, elaborate on the comparison of different measures and weight models, and present detailed hyper-parameter studies. All results are illustrated by demonstrative graphical representations.