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

2025-05-18

AI Summary

Heterogeneous graphs—characterized by significant inter-class variation in node neighborhoods—degrade GNN performance due to violated smoothness assumptions. To address this, we propose a theory-driven graph rewiring framework. First, we formally define edge homogeneity and establish its theoretical connections to embedding smoothness and downstream classification accuracy. Second, we design a label-guided diffusion mechanism to construct a high-homogeneity reference graph, and provide rigorous theoretical guarantees that rewiring improves homogeneity. The method is computationally efficient and scalable. Evaluated on 11 real-world heterogeneous graph benchmarks, it consistently outperforms state-of-the-art rewiring methods and specialized heterogeneous GNNs. Our results empirically and theoretically validate that structural optimization—via principled homogeneity enhancement—fundamentally improves GNN generalization, offering a paradigm shift from model-centric to graph-structure-centric design.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Content-based information diffusion

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.

Problem

• Improving GNN performance on heterophilic graphs
• Enhancing graph homophily via rewiring with reference graph
• Developing label-driven diffusion for homophilic reference graph construction

Innovation

• Rewiring framework enhances graph homophily
• Label-driven diffusion constructs homophilic reference graph
• Improves node classification on heterophilic graphs