arXiv subjects

Tina Šfiligoj

Publications and source records attributed to Tina Šfiligoj.

3 recordsLinked to original sources

arXiv2026

Weighted complement graphs of spatial networks with functional connections reveal nodes with high potential for new links

In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted graph $G$ is a straightforward concept, yielding a graph on the same set of nodes, and an edge exists in $\bar G$ if and only if it is not present in $G$. In contrast, a weighted complement graph cannot be uniquely determined. However, if we consider PTNs with travel times as edge weights, there are physical constraints on the possible weight ranges. We propose a method to construct weighted complement graphs of operational PTN graph representations based on the geographical distances between nodes (representing stops) and assign weights to edges based on distance, combined with network-specific distributions of effective velocities and waiting times. We observe that the most central nodes in the weighted complement graph do not correspond to the least central nodes in the original network but are, remarkably, those in the geographical centre of the network that lack topological connectedness. Testing against null models on a dataset of 31 metro networks worldwide confirms that this is a fundamentally spatial effect.

physics.soc-ph↗

arXiv2026

Access graph: a novel graph representation of public transport networks for accessibility analysis

Accessibility, defined as travel impedance between spatially dispersed opportunities for activity, is one of the main determinants of public transport use. In-depth understanding of its properties is crucial for optimal public transport systems planning and design. Although the concept has been around for decades and there is a large body of literature on accessibility operationalisation and measurement, a unified approach is lacking. To this end, we introduce a novel graph representation of public transport networks, termed the Access Graph, or A-space, based on the generalised travel times between nodes. We introduce an edge between two nodes in the access graph if the travel time between them is below a certain threshold time budget. In this representation, node degree directly measures the number of nodes reachable within a predetermined time, reproducing the cumulative opportunities measure of access at each specific value of the time budget. We study the threshold-dependent degree distribution of the access graph, focusing on the average degree and the changes in distributions between consecutive time steps. We define a set of accessibility indicators, as well as access equity indicators. The indicators are observed at two characteristic times; the first is based on the evolution of access graph topology and pertaining to the point of degree saturation, reflecting system performance, and the second from the passengers' perspective. We apply the methodology to a dataset of 51 metro networks worldwide. The new representation addresses accessibility at the network structure level, offering a conceptual framework for unified accessibility studies.

physics.soc-ph↗

arXiv2026

Multilayer public transport networks

The introduction of network science approaches into public transport research has seen great advances in the past 15 years. However, it has become apparent that monolayer networks are often not sufficient to model and analyse real-world systems in sufficient detail. In the last decade, the theory of multilayer networks has proven to be an invaluable tool in various disciplines, including transport. Multilayer networks consist of layers of networks that are coupled among themselves. This enables modelling of complex systems with heterogeneous elements and relations between them. Although there is a body of work in public transport research that uses multilayer networks, the related literature is scattered, lacking unified terminology and agreed-upon approaches. We posit that there is vast uncovered potential in using multilayer network approaches to public transport modelling, planning, and operations. We first present the basic formalisms of multilayer networks with a focus on how they (may) relate to public transport networks. We then provide a systematic review of the literature on multilayer networks in public transport research. We identify and taxonomise ways in which public transport systems are modelled as multilayer networks. Based on the survey and drawing from the state and history of network science in public transport research as well as multilayer approaches across other application domains, we propose a research agenda for multilayer public transport networks for the upcoming decade(s).

physics.soc-ph↗