Title: It Takes a Graph to Know a Graph: Rewiring for Homophily with a Reference Graph
Primary area: learning on graphs and other geometries & topologies
Keywords: graph neural networks, graph rewiring, homophily, heterophilic graphs, random walk on graphs, manifold learning

Abstract: Graph Neural Networks (GNNs) excel at analyzing graph-structured data but struggle on heterophilic graphs, where connected nodes often belong to different classes. While this challenge is commonly addressed with specialized GNN architectures, graph rewiring remains an underexplored strategy in this context. We provide theoretical foundations linking edge homophily, GNN embedding smoothness, and node classification performance, motivating the need to enhance homophily. Building on this insight, we introduce a rewiring framework that increases graph homophily using a reference graph, with theoretical guarantees on the homophily of the rewired graph. To broaden applicability, we propose a label-driven diffusion approach for constructing a homophilic reference graph from node features and training labels. Through extensive simulations, we analyze how the homophily of both the original and reference graphs influences the rewired graph homophily and downstream GNN performance. We evaluate our method on 13 real-world heterophilic datasets and show that it outperforms existing rewiring techniques and specialized GNNs for heterophilic graphs, achieving improved node classification accuracy while remaining efficient and scalable to large graphs.

TL;DR: We link node embedding smoothness, predictive performance, and homophily, proposing a rewiring framework using a reference graph constructed via label-driven diffusion, with theoretical guarantees to enhance homophily for improved GNN performance.