Graph Aggregating-Repelling Network: Do Not Trust All Neighbors in Heterophilic Graphs

Graph neural networks (GNNs) have demonstrated exceptional performance in processing various types of graph data, such as citation networks and social networks, etc. Although many of these GNNs prove their superiority in handling homophilic graphs, they often overlook the other kind of widespread heterophilic graphs, in which adjacent nodes tend to have different classes or dissimilar features. Recent methods attempt to address heterophilic graphs from the graph spatial domain, which try to aggregate more similar nodes or prevent dissimilar nodes with negative weights. However, they may neglect valuable heterophilic information or extract heterophilic information ineffectively, which could cause poor performance of downstream tasks on heterophilic graphs, including node classification and graph classification, etc. Hence, a novel framework named GARN is proposed to effectively extract both homophilic and heterophilic information. First, we analyze the shortcomings of most GNNs in tackling heterophilic graphs from the perspective of graph spectral and spatial theory. Then, motivated by these analyses, a Graph Aggregating-Repelling Convolution (GARC) mechanism is designed with the objective of fusing both low-pass and high-pass graph filters. Technically, it learns positive attention weights as a low-pass filter to aggregate similar adjacent nodes, and learns negative attention weights as a high-pass filter to repel dissimilar adjacent nodes. A learnable integration weight is used to adaptively fuse these two filters and balance the proportion of the learned positive and negative weights, which could control our GARC to evolve into different types of graph filters and prevent it from over-relying on high intra-class similarity. Finally, a framework named GARN is established by simply stacking several layers of GARC to evaluate its graph representation learning ability on both the node classification and image-converted graph classification tasks. Extensive experiments conducted on multiple homophilic and heterophilic graphs and complex real-world image-converted graphs indicate the effectiveness of our proposed framework and mechanism over several representative GNN baselines.