Is Homophily a Necessity for Graph Neural Networks?
This work re-evaluates a foundational belief in graph-based machine learning, potentially simplifying model design for heterophilous graphs, though it is incremental in refining understanding rather than introducing new methods.
The paper challenges the assumption that graph neural networks (GNNs) require homophily to perform well, showing that standard graph convolutional networks (GCNs) can achieve strong performance on heterophilous graphs under certain conditions, with empirical evidence of better performance than specialized methods on some benchmarks.
Graph neural networks (GNNs) have shown great prowess in learning representations suitable for numerous graph-based machine learning tasks. When applied to semi-supervised node classification, GNNs are widely believed to work well due to the homophily assumption ("like attracts like"), and fail to generalize to heterophilous graphs where dissimilar nodes connect. Recent works design new architectures to overcome such heterophily-related limitations, citing poor baseline performance and new architecture improvements on a few heterophilous graph benchmark datasets as evidence for this notion. In our experiments, we empirically find that standard graph convolutional networks (GCNs) can actually achieve better performance than such carefully designed methods on some commonly used heterophilous graphs. This motivates us to reconsider whether homophily is truly necessary for good GNN performance. We find that this claim is not quite true, and in fact, GCNs can achieve strong performance on heterophilous graphs under certain conditions. Our work carefully characterizes these conditions, and provides supporting theoretical understanding and empirical observations. Finally, we examine existing heterophilous graphs benchmarks and reconcile how the GCN (under)performs on them based on this understanding.