GED-Consistent Disentanglement of Aligned and Unaligned Substructures for Graph Similarity Learning

TL;DR

This paper introduces GCGSim, a novel graph similarity learning framework that aligns with the core principles of Graph Edit Distance, focusing on graph-level matching and substructure costs to improve accuracy and interpretability.

Contribution

GCGSim addresses limitations of node-centric methods by emphasizing graph-level matching and substructure costs, achieving state-of-the-art results and meaningful substructure representations.

Findings

GCGSim outperforms existing methods on four benchmark datasets.

The framework learns disentangled, semantically meaningful substructure representations.

It effectively captures global structural correspondence for optimal alignment.

Abstract

Graph Similarity Computation (GSC) is a fundamental graph related task where Graph Edit Distance (GED) serves as a prevalent metric. GED is determined by an optimal alignment between a pair of graphs that partitions each into aligned (zero-cost) and unaligned (cost-incurring) substructures. Due to NP-hard nature of exact GED computation, GED approximations based on Graph Neural Network(GNN) have emerged. Existing GNN-based GED approaches typically learn node embeddings for each graph and then aggregate pairwise node similarities to estimate the final similarity. Despite their effectiveness, we identify a mismatch between this prevalent node-centric matching paradigm and the core principles of GED. This discrepancy leads to two critical limitations: (1) a failure to capture the global structural correspondence for optimal alignment, and (2) a misattribution of edit costs driven by spurious node level signals. To address these limitations, we propose GCGSim, a GED-consistent graph similarity learning framework centering on graph-level matching and substructure-level edit costs. Specifically, we make three core technical contributions. Extensive experiments on four benchmark datasets show that GCGSim achieves state-of-the-art performance. Our comprehensive analyses further validate that the framework effectively learns disentangled and semantically meaningful substructure representations.