Node importance corresponds to passenger demand in public transport networks

Abstract

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 $\approx 0.7-0.8$). 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 ($\approx 10^{-3}$) 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.