Jiezhong He

Zhouyang Liu, Ning Liu, Yixin Chen et al.

Subgraph matching is challenging as it necessitates time-consuming combinatorial searches. Recent Graph Neural Network (GNN)-based approaches address this issue by employing GNN encoders to extract graph information and hinge distance measures to ensure containment constraints in the embedding space. These methods significantly shorten the response time, making them promising solutions for subgraph retrieval. However, they suffer from scale differences between graph pairs during encoding, as they focus on feature counts but overlook the relative positions of features within node-rooted subtrees, leading to disturbed containment constraints and false predictions. Additionally, their hinge distance measures lack discriminative power for matched graph pairs, hindering ranking applications. We propose NC-Iso, a novel GNN architecture for neural subgraph matching. NC-Iso preserves the relative positions of features by building the hierarchical dependencies between adjacent echelons within node-rooted subtrees, ensuring matched graph pairs maintain consistent hierarchies while complying with containment constraints in feature counts. To enhance the ranking ability for matched pairs, we introduce a novel similarity dominance ratio-enhanced measure, which quantifies the dominance of similarity over dissimilarity between graph pairs. Empirical results on nine datasets validate the effectiveness, generalization ability, scalability, and transferability of NC-Iso while maintaining time efficiency, offering a more discriminative neural subgraph matching solution for subgraph retrieval. Code available at https://github.com/liuzhouyang/NC-Iso.

Zhouyang Liu, Ning Liu, Yixin Chen et al.

Graph Edit Distance (GED) offers a principled and flexible measure of graph similarity, as it quantifies the minimum cost needed to transform one graph into another with customizable edit operation costs. Despite recent learning-based efforts to approximate GED via vector space representations, existing methods struggle with adapting to varying operation costs. Furthermore, they suffer from inefficient, reactive mapping refinements due to reliance on isolated node-level distance as guidance. To address these issues, we propose GEN, a novel learning-based approach for flexible GED approximation. GEN addresses the varying costs adaptation by integrating operation costs prior to match establishment, enabling mappings to dynamically adapt to cost variations. Furthermore, GEN introduces a proactive guidance optimization strategy that captures graph-level dependencies between matches, allowing informed matching decisions in a single step without costly iterative refinements. Extensive evaluations on real-world and synthetic datasets demonstrate that GEN achieves up to 37.8% reduction in GED approximation error and 72.7% reduction in inference time compared with state-of-the-art methods, while consistently maintaining robustness under diverse cost settings and graph sizes.