Improving Subgraph Matching by Combining Algorithms and Graph Neural Networks

2025-07-27

AI Summary

This paper addresses the low matching efficiency and insufficient accuracy in subgraph homomorphism—where multiple vertices in the pattern graph may map to the same vertex in the target graph. We propose HFrame, the first unified framework integrating classical graph matching algorithms with graph neural networks (GNNs). Our contributions are threefold: (1) We pioneer the incorporation of GNNs into subgraph homomorphism, enabling end-to-end learning to enhance structural discriminability; (2) we derive a theoretically grounded, generalized error upper bound; and (3) we design a differentiable matching module that enables joint optimization of traditional algorithms and deep learning components. Extensive experiments on real-world and synthetic graph datasets demonstrate that HFrame achieves up to 101.91× speedup in matching time and attains an average accuracy of 0.962, significantly outperforming state-of-the-art methods.

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Homomorphism is a key mapping technique between graphs that preserves their structure. Given a graph and a pattern, the subgraph homomorphism problem involves finding a mapping from the pattern to the graph, ensuring that adjacent vertices in the pattern are mapped to adjacent vertices in the graph. Unlike subgraph isomorphism, which requires a one-to-one mapping, homomorphism allows multiple vertices in the pattern to map to the same vertex in the graph, making it more complex. We propose HFrame, the first graph neural network-based framework for subgraph homomorphism, which integrates traditional algorithms with machine learning techniques. We demonstrate that HFrame outperforms standard graph neural networks by being able to distinguish more graph pairs where the pattern is not homomorphic to the graph. Additionally, we provide a generalization error bound for HFrame. Through experiments on both real-world and synthetic graphs, we show that HFrame is up to 101.91 times faster than exact matching algorithms and achieves an average accuracy of 0.962.

Problem

• Enhancing subgraph homomorphism via algorithm-GNN fusion
• Solving complex pattern-graph mapping with HFrame
• Boosting speed and accuracy in subgraph matching

Innovation

• Combines traditional algorithms with graph neural networks
• Introduces HFrame for subgraph homomorphism
• Achieves high speed and accuracy in matching