We propose a topological formulation of accessibility based on the notion of Access Graph, in which two nodes are connected if they are reachable within a given travel time. We trace the emergence and evolution of its subgraphs with imposed levels of connectedness, specifically maximal clique and k-cores. We propose two complementary sets of accessibility indicators, cumulative and threshold, based on integral measures of subgraph growth and times at emergence of k-cores, respectively. For a meaningful comparison of networks across different dimensions, we contrast the realised accessibility with that of an idealised network on the same set of nodes. The proposed measures offer a view of accessibility that extends beyond the commonly used node-averaged indicators. Empirical analysis of 42 metro networks worldwide demonstrates universal patterns of accessibility behaviour. We illustrate the practical application of this approach on a case study where we examine the accessibility impacts yielded by alternative infrastructure and service developments. Our results amount to the reconceptualisation of accessibility within the complex network framework.

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 standardised approach is lacking. To this end, we introduce a dedicated 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 evolution of the degree distribution of the access graph and define a set of accessibility indicators. The indicators are observed at network-specific and passenger-based characteristic times. We apply the methodology to a dataset of 51 metro networks worldwide. For the Washington DC metro, we validate the approach by comparing supply to demand at the origin–destination level. The new representation addresses accessibility at the network structure level, offering a network science-grounded and flexible conceptual framework for accessibility studies.

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.