H \(^2\) GNN: Graph Neural Networks with Homophilic and Heterophilic Feature Aggregations

Graph neural networks (GNNs) rely on the assumption of graph homophily, which, however, does not hold in some real-world scenarios. Graph heterophily compromises them by smoothing node representations and degrading their discrimination capabilities. To address this limitation, we propose H \(^2\) GNN, which implements Homophilic and Heterophilic feature aggregations to advance GNNs in graphs with homophily or heterophily. H \(^2\) GNN proceeds by combining local feature separation and adaptive message aggregation, where each node separates local features into similar and dissimilar feature vectors, and aggregates similarities and dissimilarities from neighbors based on connection property. This allows both similar and dissimilar features for each node to be effectively preserved and propagated, and thus mitigates the impact of heterophily on graph learning process. As dual feature aggregations introduce extra model complexity, we also offer a simplified implementation of H \(^2\) GNN to reduce training time. Extensive experiments on seven benchmark datasets have demonstrated that H \(^2\) GNN can significantly improve node classification performance in graphs with different homophily ratios, which outperforms state-of-the-art GNN models.