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