Modeling CitiBike Mobility as a Directed Graph with Magnetic Laplacian-Based Graph Neural Networks

Abstract

Urban transportation networks are fundamentally directed: riders flow from residential zones to business districts in the morning and back in the evening, but detours and changes in routine prevent perfect reciprocality. This creates asymmetric trip patterns that conventional undirected methods cannot represent. This thesis applies the magnetic Laplacian, a complex Hermitian operator encoding undirected structure in entry magnitudes and directed structure in complex phase terms, to model NYC CitiBike mobility as a directed weighted graph. Utilizing approximately 1.8 million trips from January 2023 across 1,760 stations and 334,875 edges, we perform analysis spanning classical network metrics, spectral analysis, and MagNet flow prediction. Local network analysis revealed strong directional asymmetries, with residential zones as net exporters and commercial areas as net absorbers of riders. Spectral analysis on a subgraph of 311 high-traffic stations identified ∼32 directional flow regimes, recovering otherwise invisible cross-borough commuter corridors. MagNet on the full graph achieved a validation correlation of 0.633 on log-transformed trip counts, substantially outperforming a global mean predictor and linear regression baseline. A sweep over the magnetic charge parameter q confirmed that removing the directional phase reduced correlation from 0.470 to 0.345 for the subgraph. It also identified q = 0.40 as optimal, higher than the default of 0.25 in prior literature, suggesting it should be treated as a domain-specific hyperparameter. Cross-month generalization to February 2023 yielded 0.603, while cross-year generalization to January 2024 achieved 0.461, likely due to CitiBike’s nearly 30% year-over-year station expansion. These results establish that the magnetic Laplacian captures directional mobility structure meaningfully for large-scale prediction, contributing to directed graph learning and providing a foundation for CitiBike’s re-balancing and planning operations.