Neighbors selective Graph Convolutional Network for homophily and heterophily

Graph Convolutional Networks (GCNs) gain remarkable success in graph-related tasks under homophily graph assumption—most connected nodes have the same label. However, this assumption is fragile since heterophily is common in real-world networks, where most linked nodes have different labels. Some methods address heterophily using graph-level weighted combinations of multi-hop neighbor representations. However, they introduce noise and irrelevant information from two aspects: (1) higher-order neighborhoods may include more neighbors with different labels than those with the same label; (2) graph-level weighted combination fails to capture distinct node properties. To address these issues, firstly, a Neighborhood Distribution-induced Similarity (NDS) measure is developed to identify potential similar neighbors for nodes. Secondly, a node-level fusion mechanism Selective-Neighbors Gated Unit (SNGU) is designed to adaptively aggregate potential neighbors, first-hop neighbors, and the node itself by learning distinct weights for nodes. By combining the above two designs, this work proposes a novel Neighbors Selective Graph Convolutional Network (NSGCN), which allows nodes to selectively receive relevant neighbor information for better node representations, effectively modeling homophily and heterophily. Experiments on 10 widely used real-world datasets with varying properties demonstrate the superiority of the NSGCN, surpassing a strong baseline with an absolute increase of 9.83% in classification accuracy. The code is available at https://github.com/GGA23/NSGCN.