Hybrid Diffusion–Transport GNNs on Directed Graphs

Directionality is intrinsic to many graph-structured systems, yet the resulting asymmetric operators complicate the spectral foundations of classical graph neural networks. Hermitian Laplacians address this limitation by encoding edge direction through complex-valued phase information while retaining real eigenvalues and a unitary eigenbasis. We reinterpret this construction through a diffusion–transport decomposition, in which the real component captures symmetric diffusion and the imaginary component represents directional transport. Building on this interpretation, we introduce ArcShift, a first-order approximation of the magnetic phase that yields an explicit diffusion–transport propagation operator. We further propose ArcShift-CVNN, a complex-valued extension that jointly transforms the real and imaginary feature representations. Experiments on multiple directed graph benchmarks evaluate the proposed models against the exact magnetic formulation and representative graph-learning baselines in terms of node-classification performance and computational behavior. Overall, ArcShift provides an efficiency- and interpretability-oriented directional propagation operator while maintaining competitive predictive performance.