Flow Matters: Directional and Expressive GNNs for Heterophilic Graphs
This work addresses the problem of improving classification accuracy in heterophilic graphs for researchers and practitioners in graph machine learning, though it is incremental by building on prior studies of directionality and expressive GNNs.
The paper tackled node classification in heterophilic graphs by combining edge directionality and expressive message passing, resulting in state-of-the-art performance on benchmark datasets, with the Dir-Poly model achieving additional gains on graphs with inherent directionality.
In heterophilic graphs, where neighboring nodes often belong to different classes, conventional Graph Neural Networks (GNNs) struggle due to their reliance on local homophilous neighborhoods. Prior studies suggest that modeling edge directionality in such graphs can increase effective homophily and improve classification performance. Simultaneously, recent work on polynomially expressive GNNs shows promise in capturing higher-order interactions among features. In this work, we study the combined effect of edge directionality and expressive message passing on node classification in heterophilic graphs. Specifically, we propose two architectures: (1) a polynomially expressive GAT baseline (Poly), and (2) a direction-aware variant (Dir-Poly) that separately aggregates incoming and outgoing edges. Both models are designed to learn permutation-equivariant high-degree polynomials over input features, while remaining scalable with no added time complexity. Experiments on five benchmark heterophilic datasets show that our Poly model consistently outperforms existing baselines, and that Dir-Poly offers additional gains on graphs with inherent directionality (e.g., Roman Empire), achieving state-of-the-art results. Interestingly, on undirected graphs, introducing artificial directionality does not always help, suggesting that the benefit of directional message passing is context-dependent. Our findings highlight the complementary roles of edge direction and expressive feature modeling in heterophilic graph learning.