Revisit bus network robustness from the perspective of service-physical dependency

This study revisits bus network robustness by addressing the dependency of bus service networks on the underlying physical road network. A novel methodology integrates resistance distance theory with a multilayer physical-service network framework, accounting for disruptions at the road layer and detour mechanisms. Two robustness indices are introduced: the absolute resistance robustness index, which quantifies the overall impact of disruptions, and the relative resistance robustness index, which reflects network redundancy. Using data from 29 cities, the empirical analysis reveals that geographical and socioeconomic factors significantly influence bus network robustness, with higher GDP, flatter terrains, and concentrated urban areas associated with greater relative robustness. Sensitivity analysis identifies terrain compactness as the most influential factor. This methodology advances the theoretical understanding of transportation network resilience and provides practical tools for urban transportation planning. Future research could extend the approach to directional networks and incorporate travel demand data for more refined analyses.