Unveiling the Impact of Local Homophily on GNN Fairness: In-Depth Analysis and New Benchmarks

Graph Neural Networks (GNNs) often struggle to generalize when graphs exhibit both homophily (same-class connections) and heterophily (different-class connections). Specifically, GNNs tend to underperform for nodes with local homophily levels that differ significantly from the global homophily level. This issue poses a risk in user-centric applications where underrepresented homophily levels are present. Concurrently, fairness within GNNs has received substantial attention due to the potential amplification of biases via message passing. However, the connection between local homophily and fairness in GNNs remains underexplored. In this work, we move beyond global homophily and explore how local homophily levels can lead to unfair predictions. We begin by formalizing the challenge of fair predictions for underrepresented homophily levels as an out-of-distribution (OOD) problem. We then conduct a theoretical analysis that demonstrates how local homophily levels can alter predictions for differing sensitive attributes. We additionally introduce three new GNN fairness benchmarks, as well as a novel semi-synthetic graph generator, to empirically study the OOD problem. Across extensive analysis we find that two factors can promote unfairness: (a) OOD distance, and (b) heterophilous nodes situated in homophilous graphs. In cases where these two conditions are met, fairness drops by up to 24% on real world datasets, and 30% in semi-synthetic datasets. Together, our theoretical insights, empirical analysis, and algorithmic contributions unveil a previously overlooked source of unfairness rooted in the graph's homophily information.