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

Abstract

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.

Figures (11)

• Figure 1: Overview of existing PTN graph representations and placement of our new A-space representation in the group.
• Figure 2: A visualization of the time budget-dependent access graph for the Oslo metro. In successive subplots, access graphs at respective values of $t_b$, as indicated in each subplot title, are shown. The edges that first appear at a given $t_b$ are shown in red. Other edges (i.e., those present in $\mathcal{G}_A$ already earlier than at $t_b$) are shown in grey. The Oslo metro has $N=101$ nodes and a maximum generalised travel time of $t_{max} = 92$ min.
• Figure 3: A visualization of the time budget-dependent access graph for the Vienna metro. In successive subplots, access graphs at respective values of $t_b$, as indicated in each subplot title, are shown. The edges that first appear at any given $t_b$ are shown in red. Other edges (i.e., those present in $\mathcal{G}_A$ already earlier than at $t_b$) are shown in grey. In each subplot, the degree distribution of $\mathcal{G}_A$ is shown in the inset plot. The Vienna metro has $N=98$ nodes and a maximum generalised travel time of $t_{max} = 74$ min.
• Figure 4: Heatmaps of degree distributions with varying time budgets for the Oslo (left) and Vienna (right) metros. $t_b$ is increased in steps of 2 minutes. The $x$-axis represents the time budget, and the $y$-axis represents the node degree in the respective access graph. Heatmap cell color represents the percentage of nodes in each degree bin. Thus, each vertical column represents the color-coded histogram of the node degree distribution. The average degree at each $t_b$ bin is plotted with red markers.
• Figure 5: Oslo (left) and Vienna (right).