Graph representation learning aim at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that many existing graph learning methods do not work well on data with high heterophily level that accounts for a large proportion of edges between different class labels. Recent efforts to this problem focus on improving the message passing mechanism. However, it remains unclear whether heterophily truly does harm to the performance of graph neural networks (GNNs). The key is to unfold the relationship between a node and its immediate neighbors, e.g., are they heterophilous or homophilious? From this perspective, here we study the role of heterophily in graph representation learning before/after the relationships between connected nodes are disclosed. In particular, we propose an end-to-end framework that both learns the type of edges (i.e., heterophilous/homophilious) and leverage edge type information to improve the expressiveness of graph neural networks. We implement this framework in two different ways. Specifically, to avoid messages passing through heterophilous edges, we can optimize the graph structure to be homophilious by dropping heterophilous edges identified by an edge classifier. Alternatively, it is possible to exploit the information about the presence of heterophilous neighbors for feature learning, so a hybrid message passing approach is devised to aggregate homophilious neighbors and diversify heterophilous neighbors based on edge classification. Extensive experiments demonstrate the remarkable performance improvement of GNNs with the proposed framework on multiple datasets across the full spectrum of homophily level.

Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.

Graph Neural Networks (GNNs) aim at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that most of existing GNNs do not work well on data with high heterophily level that accounts for a large proportion of edges between different class labels. Recently, many efforts to tackle this problem focus on optimizing the way of feature learning. From another angle, this work aims at mitigating the negative impacts of heterophily by optimizing graph structure for the first time. Specifically, on assumption that graph smoothing along heterophilious edges can hurt prediction performance, we propose a structure learning method called LHE to identify heterophilious edges to drop. A big advantage of this solution is that it can boost GNNs without careful modification of feature learning strategy. Extensive experiments demonstrate the remarkable performance improvement of GNNs with LHE on multiple datasets across full spectrum of homophily level.