DiRW: Path-Aware Digraph Learning for Heterophily

Recently, graph neural network (GNN) has emerged as a powerful representation learning tool for graph-structured data. However, most approaches are tailored for undirected graphs, neglecting the abundant information embedded in the edges of directed graphs (digraphs). In fact, digraphs are widely applied in the real world (e.g., social networks and recommendations) and are also confirmed to offer a new perspective for addressing topological heterophily challenges (i.e., connected nodes have complex patterns of feature distribution or labels). Despite recent significant advancements in DiGNNs, existing spatial- and spectral-based methods have inherent limitations due to the complex learning mechanisms and reliance on high-quality topology, leading to low efficiency and unstable performance. To address these issues, we propose Directed Random Walk (DiRW), which can be viewed as a plug-and-play strategy or an innovative neural architecture that provides a guidance or new learning paradigm for most spatial-based methods or digraphs. Specifically, DiRW incorporates a direction-aware path sampler optimized from the perspectives of walk probability, length, and number in a weight-free manner by considering node profiles and topological structure. Building upon this, DiRW utilizes a node-wise learnable path aggregator for generalized messages obtained by our proposed adaptive walkers to represent the current node. Extensive experiments on 9 datasets demonstrate that DiRW: (1) enhances most spatial-based methods as a plug-and-play strategy; (2) achieves SOTA performance as a new digraph learning paradigm.