On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks

Research on GNNs has highlighted a relationship between high homophily (i.e., the tendency for nodes of a similar class to connect) and strong predictive performance in node classification. However, recent research has found the relationship to be more nuanced, demonstrating that even simple GNNs can learn in certain heterophilous settings. To bridge the gap between these findings, we revisit the assumptions made in previous works and identify that datasets are often treated as having a constant homophily level across nodes. To align closer to real-world datasets, we theoretically and empirically study the performance of GNNs when the local homophily level of a node deviates at test-time from the global homophily level of its graph. To aid our theoretical analysis, we introduce a new parameter to the preferential attachment model commonly used in homophily analysis to enable the control of local homophily levels in generated graphs, enabling a systematic empirical study on how local homophily can impact performance. We additionally perform a granular analysis on a number of real-world datasets with varying global homophily levels. Across our theoretical and empirical results, we find that (a)~ GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, (b)~ high local homophily does not necessarily confer high performance for a node, and (c)~ GNN models designed to handle heterophily are able to perform better across varying heterophily ranges irrespective of the dataset's global homophily. These findings point towards a GNN's over-reliance on the global homophily used for training and motivates the need to design GNNs that can better generalize across large local homophily ranges.