DCGNN: Adaptive deep graph convolution for heterophily graphs

Abstract

Graph neural networks (GNNs) have demonstrated significant efficacy in addressing graph learning tasks by leveraging both node features and graph topology. Prevalent GNN architectures often implicitly or explicitly rely on the homophily assumption, which presupposes that neighboring nodes tend to share similar features. Despite their efficacy, GNNs may prove inadequate in modeling graphs characterized by heterophily, wherein nodes with disparate labels frequently interconnect. To mitigate this limitation, we propose DCGNN, a novel GNN framework capable of accommodating heterophily while retaining effectiveness in homophily scenarios. Initially, we elucidate that prevailing message-passing neural networks (MPNNs) struggle to discern circular substructures, prevalent in graphs demonstrating heterophily. Consequently, we propose an adaptive deep graph convolution technique, which integrates adaptive aggregation of local high-order neighborhoods, replacing the conventional stacking of single-order convolutional layers in the message-passing paradigm. Theoretical analysis confirms that DCGNN demonstrates significantly enhanced expressive capacity compared to existing MPNNs. Empirical evaluations conducted on real-world datasets validate that DCGNN outperforms several state-of-the-art GNNs tailored for graphs exhibiting heterophily.