  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.
