On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks

TL;DR

This paper investigates how local variations in homophily within graphs affect GNN performance, revealing that local homophily deviations can cause performance gaps and proposing GNNs for heterophilous graphs to improve robustness.

Contribution

It introduces a systematic analysis of local homophily effects on GNN performance, combining theoretical and empirical insights, and suggests new GNN designs for heterophilous graphs.

Findings

Local homophily deviations can cause significant performance drops.

High local homophily does not always mean better node classification.

Heterophilous GNNs improve performance across diverse local homophily levels.

Abstract

Graph Neural Network (GNN) research has highlighted a relationship between high homophily (i.e., the tendency of nodes of the same class to connect) and strong predictive performance in node classification. However, recent work has found the relationship to be more nuanced, demonstrating that simple GNNs can learn in certain heterophilous settings. To resolve these conflicting findings and align closer to real-world datasets, we go beyond the assumption of a global graph homophily level and study the performance of GNNs when the local homophily level of a node deviates from the global homophily level. Through theoretical and empirical analysis, we systematically demonstrate how shifts in local homophily can introduce performance degradation, leading to performance discrepancies across local homophily levels. We ground the practical implications of this work through granular analysis on five real-world datasets with varying global homophily levels, demonstrating that (a) GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, and (b) high local homophily does not necessarily confer high performance for a node. We further show that GNNs designed for globally heterophilous graphs can alleviate performance discrepancy by improving performance across local homophily levels, offering a new perspective on how these GNNs achieve stronger global performance.