Is Homophily a Necessity for Graph Neural Networks?

TL;DR

This paper challenges the belief that homophily is essential for GNN success, showing that standard GCNs can perform well on heterophilous graphs under certain conditions through theoretical and empirical analysis.

Contribution

It demonstrates that homophily is not strictly necessary for GNN effectiveness and characterizes conditions under which GCNs excel on heterophilous graphs, supported by theory and experiments.

Findings

GCNs can outperform specialized heterophily methods on some datasets

Homophily is not a strict requirement for GNN success

Conditions for GCN effectiveness on heterophilous graphs are identified

Abstract

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.