Electric-circuit reconstruction of urban bus passenger loads on service-frequency-weighted networks

Detailed origin–destination records provide direct information on public transport use, but their public release is often restricted because they contain sensitive mobility information. This raises a simple question: how much aggregate information is actually needed to reconstruct passenger loads on a bus network? Using bus origin–destination data from Hirosaki, Japan, we separate passenger movements into flows travelling outward from the core station and flows travelling toward it. Boarding–alighting imbalances at stops define source–sink fields, while empirical service frequencies define route-segment conductances. Solving the resulting conductance-weighted graph Poisson equation yields edge currents interpreted as reconstructed passenger loads. To clarify the domain of applicability of the model, we compared reconstructions using datasets that included and excluded circular and circular-like routes. With the full source–sink field, the baseline directional dataset retained 93.3% of the valid OD records and yielded R²=0.901 for and R²=0.818 for . After excluding circular and circular-like routes, the retained coverage decreased to 60.0%, while R² increased to 0.989 for and 0.963 for . Cross-period reconstruction between the first and second halves of June and December yielded R²=0.970 –0.983 for and 0.938–0.965 for on the non-circular network. Even when only the core-station source–sink imbalance was provided, the model reproduced a substantial part of the spatial load distribution without post-hoc scaling, with R²=0.907 for and 0.768 for . The framework was additionally applied to Goshogawara, where the CORE-only reconstruction yielded R²=0.456 for and R²=-0.016 for , reflecting the weaker dominance of the station core. These results identify predominantly radial, non-circular bus networks as the principal domain of the present electric-circuit formulation and show that CORE-only reconstruction is most effective when the selected station core is dominant.