Flexible Graph Similarity Computation With A Proactive Optimization Strategy

TL;DR

This work tackles flexible GED approximation by introducing GEN, which (1) integrates operation costs before mapping to adapt mappings to cost settings, and (2) employs a proactive guidance strategy that propagates graph-level alignment difficulties for informed one-shot matching. The approach combines a shared GNN encoder, cost-sensitive scoring via an Estimator, and difficulty propagation to produce graph-level guidance, significantly reducing GED approximation error and inference time while remaining robust to varying graph sizes and cost settings. Empirical results on real-world and synthetic data show substantial gains over state-of-the-art methods, with strong adaptability to non-uniform costs and improved scalability. The proposed method has practical implications for fast, accurate graph retrieval and reranking in systems where edit operations carry different semantic costs.

Abstract

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.

Figures (9)

• Figure 1: The black dashed lines are matches, and the red markings are edits. $f_1$ and $f_2$ are mappings. $f_1$ incurs 2 node substitutions (ns), 1 node insertion, 1 edge deletion, and 2 edge insertions (ei), denoted as $[2, 1, 0, 1, 2]$, while $f_2$ incurs $[4, 1, 0, 0, 1]$. When ns costs 2, other operations cost 1, $f_1$ is optimal with a cost of 8, while $f_2$ costs 10. However, if ei costs 2, others cost 1, $f_1$ costs 8 while $f_2$ costs 7, making $f_2$ the optimal choice.
• Figure 2: Models marked with ‘*’ perform only a single round of refinement.
• Figure 3: Overview of Gen. The dashed node represents the dummy node.
• Figure 4: Time Efficiency of GSC models. The bars with black edges represent node comparison-based methods.
• Figure 5: Performance of models on larger synthetic graphs across diverse node size groups.