Learning Graph Shift Operator for Directed Graphs

Directed graphs arise naturally in many realworld applications, yet most graph neural networks are designed for undirected settings. This paper proposes a graph neural network framework that jointly learns a directionaware graph shift operator and network parameters, enabling expressive feature propagation while preserving edge directionality. By maintaining separate learnable parameters for incoming and outgoing propagation, the framework allows the model to adaptively capture distinct directional roles of nodes and balance information flow across both directions. Experiments on benchmark directed datasets demonstrate consistent performance gains over existing baselines, particularly on homophilous directed graphs.