Node importance corresponds to passenger demand in public transport networks

Šfiligoj, Tina (author), Peperko, Aljoša (author), Bajec, Patricija (author), Cats, Oded (author)

We investigate the correspondence between network-based public transport network (PTN) supply indicators and passenger demand at the node level, by systematically assessing correlations between node centrality measures and passenger boarding counts across different graph representations of PTNs. At the stop-level, undirected L- and P-space representations with three different edge weightings: unweighted, service-frequency-weighted, and in-vehicle-time-weighted are analysed. In each case, we calculate degree, closeness, betweenness and eigenvector centralities and examine the relation shapes. At the route level, we examine degree and eigenvector centrality for unweighted and weighted C-space representations. We introduce a modified C-space representation with self-loops, with service frequencies as self-loop weights, and propose eigenvector centrality as a route-level supply indicator. Stop- and route-level properties are integrated using the B-space representation. This methodology was applied to a case study for a bus PTN in Ljubljana, Slovenia. Results show strong correspondence between passenger demand and degree and eigenvector centrality scores in the frequency-weighted P-space (correlation ≈ 0.7 − 0.8). Notably, the relationship between eigenvector centrality and passenger counts in the new C-space representation with self-loops exhibits logarithmic behaviour. Furthermore, the results suggest a minimum eigenvector centrality threshold (≈ 10$^{−3}$) for a route to start facilitating passenger use. The route-level results from the B-space analysis show exponential convergence of passenger counts to route eigenvector centrality. Results of the stop-level analysis are in line with previous research and deepen the understanding of centrality measures as supply indicators. Most significantly, the route-level analysis is novel, and the results open promising venues for further research.

• Language: English
• Keywords: public transport, graph theory, network science, General Transit Feed Specification, GTFS, smart card data, node centrality
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FPP - Faculty of Maritime Studies and Transport; FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 18 str.
• Numbering: Vol. 659, art. 130354
• PID: 20.500.12556/RUL-166865
• UDC: 519.17:004
• ISSN on article: 0378-4371
• DOI: 10.1016/j.physa.2025.130354
• COBISS.SI-ID: 221377539
• Publication date in RUL: 28.01.2025

Record is a part of a journal

• Title: Physica. A, Statistical mechanics and its applications
• Shortened title: Physica, A
• Publisher: Elsevier
• ISSN: 0378-4371
• COBISS.SI-ID: 3270415

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: javni prevoz, teorija grafov, znanost o omrežjih, splošne specifikacije tranzitnega vira, GTFS, podatki pametne kartice

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0394
• Name: Modeliranje in simulacije v prometu in pomorstvu

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika