MetroVFE: A Vitality–Function–Spatial Coverage Equity Coupling-Coordination Framework for Diagnosing Metro-Station Structural Service Potential from Multimodal Transit Network Topology

Comparing metro-station service at national scale is hindered by the scarcity of consistent ridership or mobile-phone data across cities. We propose MetroVFE, a topology-based framework for diagnosing metro-station structural service potential. It combines three coupled subsystems—vitality (network centrality, transfer capacity, and feeder-bus connectivity), function (route-type diversity, destination reachability, directional coverage, and operator diversity), and spatial coverage equity (station-spacing uniformity). All indicators are derived from publicly available transit-network topology. Each subsystem is aggregated by entropy weighting, and the three are combined through a coupling coordination degree (CCD) model that penalizes unbalanced development. We instantiate the framework on the CPTOND-2025 national bus–metro vector dataset, computing indicators for 7057 unique metro stations in 45 Chinese cities, with 42,796 feeder bus routes spatially joined to 500 m station catchments. The empirical analysis yields four main findings: (i) Coupling coordination is moderate and has positive skew: the mean station CCD is 0.46, with 58.5% of stations in antagonistic or transitional bands and only 1.5% highly coordinated. (ii) vitality is the dominant lagging subsystem (66.4% of stations), and this share rises monotonically from large to small networks (63.7%→69.3%→78.2%). (iii) Unsupervised clustering recovers five interpretable diagnostic typologies, dominated by vitality-deficient (48.3%) and function-developing (24.8%) stations, with only 12.3%balanced–coordinated. (iv) Spatial coverage equity modestly moderates the function→vitality relationship (interaction p=1×10−4, robust to controls): the marginal contribution of functional diversity to vitality is about 25% larger in high-coverage-equity than low-coverage-equity station areas (0.207 vs. 0.165). Mean coordination does not differ significantly across network-size tiers (ANOVA p=0.12), but typology composition does (χ2p<10−58). Ablation and sensitivity analyses confirm that the coordination feature and the full V-F-E feature set are necessary for stable typologies. MetroVFE is fully reproducible from open data and provides an actionable, mathematically grounded tool for prioritizing station-level interventions.