Title: Enhancing Combinatorial Graph Alignment via Sequential 2-FWL GNNs

Abstract:

In the realm of combinatorial graph alignment problems (GAP)—which aim to identify node correspondences that maximize the count of shared edges, or nce, between two unlabeled graphs—properly initialized FAQ continues to serve as a robust classical baseline. Conversely, current Graph Neural Network (GNN) methodologies often falter in purely structural contexts. To address this, we propose a chaining methodology that employs a sequence of Folklore-type (2-FWL) GNNs. In this framework, each network is trained using cross-entropy loss; this process follows the decoding of the preceding network’s similarity matrix and involves ranking nodes based on their current alignment quality. This specific ranking step is non-differentiable, thereby introducing discrete combinatorial feedback at each connection. During inference, the final network is iterated, and the candidate yielding the highest observed nce is selected.

Our empirical results demonstrate significant improvements over existing methods. On sparse Erdos-Renyi graphs with a noise level of 0.25, chained FGNNs combined with FAQ post-processing achieved an accuracy of 85%. This stands in stark contrast to the 13% accuracy of FAQ when initialized via convex relaxation, and the near-zero performance of previous GNN approaches. Furthermore, on correlated regular graphs, where Message Passing GNNs (MPNNs) with constant features generate identical node embeddings—rendering 1-WL refinement ineffective—and where FAQ’s convex initialization becomes degenerate, chaining remains the sole known technique capable of recovering a non-trivial alignment.

Finally, our evaluation across three real-world benchmarks—yeast PPI, coauthorship, and road networks—reveals that recent studies may underestimate FAQ’s capabilities by initializing it from a uniform doubly stochastic matrix. When FAQ is instead initialized using convex relaxation, it already outperforms previously reported figures. Moreover, employing dataset-specific chained FGNNs yields further enhancements upon this strengthened baseline.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC