It Takes a Graph to Know a Graph: Rewiring for Homophily with a Reference Graph

TL;DR

This work tackles poor GNN performance on heterophilic graphs by introducing a principled rewiring strategy guided by a reference graph to boost edge homophily. It establishes theoretical links between homophily, embedding smoothness, and classification accuracy, and proposes a diffusion-based method to construct a homophilic reference graph from node features and training labels. The proposed REFine framework applies cluster-wise rewiring with reference-driven edge additions or deletions, backed by theoretical guarantees under certain conditions and validated across 11 real-world heterophilic datasets. Empirically, REFine often surpasses specialized heterophilic GNNs and existing rewiring methods while maintaining scalability, highlighting its practical impact for robust node classification in challenging graph regimes.

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 11 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.

Figures (11)

• Figure 1: Edge addition on Cornell: First row shows homophily increases with $k$ when the condition holds (blue above red); second row shows its impact on GCN accuracy. $H(\mathcal{G}_{r,p})$ decreases from left to right across the columns.
• Figure 2: Edge deletion on Cora: Homophily increases when the condition is met (green line below red).
• Figure 3: Rewiring method overview: (1) Cluster the original graph into clusters. (2) Construct a reference graph for each cluster using node features (yellow rectangles) and available labels (red squares). (3) Rewire each cluster by modifying edges based on its reference graph. (4) Reconstruct the fully rewired graph by incorporating inter-cluster edges. We denote the $i$-th cluster as $\mathcal{G}_i$, its reference graph as $\mathcal{G}_{i,r}$, and the rewired cluster as $\mathcal{G}_i^{(k)}$.
• Figure 4: Rewiring Cora using $\mathcal{G}_r$ built only from train labels.
• Figure 5: Simulation of edge addition on the Wisconsin dataset.

Theorems & Definitions (7)

• Theorem 1
• Proposition 1
• Corollary 1
• Proposition 2
• proof : Proof of Theorem \ref{['smoothness-theo-1']}
• proof : Proof of Proposition \ref{['homo-theo-add-1']}
• proof : Proof of Proposition \ref{['homo-theo-delete-1']}