DsrFGW Enhances Graph Comparison with Diffusion Processes

Comparing graphs, especially those that are sparse, noisy, or incomplete, is a significant challenge in many fields. Traditional methods like Gromov-Wasserstein (GW) and its semi-relaxed variants (srGW, srFGW) capture graph structure but often struggle under these difficult conditions. The core limitation is their sensitivity to noise and missing information. Inspired by the concept of Graph Diffusion Distance, which suggests that similar graphs facilitate similar information flow, a new method called Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW) has been developed. DsrFGW incorporates diffusion processes, allowing information to propagate across nodes. This mechanism helps capture both local and global structural patterns more effectively, while simultaneously reducing the method's sensitivity to noise or missing edges. Extensive evaluations across 36 synthetic graph matching tasks demonstrated DsrFGW's consistent superiority. It achieved accuracy improvements of up to 20 percentage points over srFGW and dramatic gains in Adjusted Rand Index (ARI), often turning srFGW's negative ARI (worse than random) into positive performance. DsrFGW proved robust even under severe noise, improving clustering quality in 92% of tasks, establishing it as a powerful framework for graph comparison under structural uncertainty.