confidence-weighted graph matching

This work addresses the graph alignment problem for sparse random geometric graphs with binary vertex features subject to noise: given two independently perturbed graphs, the goal is to recover the unknown vertex correspondence. We propose a novel alignment method based on a single-layer graph neural network (GNN) and provide the first theoretical guarantee showing that it achieves exact recovery with high probability even when feature noise scales as a power law in the graph size—up to a tight logarithmic factor. In contrast, classical alignment algorithms relying on clean features fail under constant-level noise. Our analysis integrates random geometric graph modeling with rigorous characterization of noisy binary features. Experiments confirm that the proposed method significantly outperforms baseline approaches, including direct feature matching.

This paper addresses graph alignment—a computationally intractable (NP-hard) combinatorial optimization problem involving node matching across unlabeled graphs using structural information only. We propose Chain-GNN, a novel chained-training sequential graph neural network. Methodologically, it integrates node-pair-level global modeling, bootstrapped iterative training, discrete ranking feedback, and combinatorial optimization-based post-processing to jointly optimize a structure-aware similarity matrix. Our key contribution is the first successful突破 of the regularized graph alignment bottleneck: on synthetic benchmarks, Chain-GNN achieves over a threefold improvement in alignment accuracy compared to prior state-of-the-art solvers. This work establishes a new paradigm for deploying GNNs in practical combinatorial optimization tasks, demonstrating both theoretical advancement and empirical superiority.

This work addresses two critical challenges in graph neural network (GNN) evaluation: the absence of a universal benchmark and the low learning efficiency of positional encodings. To this end, we propose the first GNN evaluation framework that employs graph alignment as a self-supervised pretraining task. The framework supports systematic assessment of GNN architectures by generating multi-difficulty alignment datasets—both synthetic and real-world. Crucially, we formulate graph alignment as a general-purpose benchmark task and demonstrate, for the first time, its effectiveness in learning high-quality positional encodings: our method achieves state-of-the-art performance on the PCQM4Mv2 molecular property regression task with significantly fewer parameters. Moreover, anisotropic GNNs consistently outperform standard graph convolutional models on alignment tasks. To ensure reproducibility and broad adoption, we open-source a comprehensive toolkit for dataset generation and model evaluation.

This work addresses the limited expressive power of unsupervised graph alignment models, particularly in discriminating matching versus non-matching node pairs and enforcing structural matching constraints (e.g., bijectivity and mutual alignment). We propose CombAlign, a theoretically grounded hybrid framework that— for the first time—formalizes model expressivity from both discriminative capability and matching constraint perspectives. CombAlign integrates Gromov–Wasserstein optimal transport with Weisfeiler–Lehman-style node embedding, incorporates non-uniform marginal priors to encode structural biases, and refines alignments via maximum-weight bipartite matching. Evaluated on standard benchmarks, CombAlign achieves a 14.5% absolute improvement in alignment accuracy over state-of-the-art methods. Empirical results consistently validate the theoretical analysis, demonstrating strong alignment between expressivity characterization and practical performance.

This paper investigates the fundamental limits and algorithmic design for exact node matching across multiple correlated graphs, addressing the information-theoretic bottleneck preventing exact recovery in the sparse regime for pairwise graph matching. Method: We propose the first globally consistent, transitivity-enforced stepwise matching algorithm that achieves the information-theoretic lower bound. Our approach integrates k-core pruning, joint likelihood estimation, and transitive alignment; it further derives novel structural properties of the k-core in Erdős–Rényi graphs. Contribution/Results: Theoretically, we establish the first necessary and sufficient condition for exact multi-graph matching, proving that three or more correlated graphs strictly expand the solvable regime beyond pairwise matching. Experimentally and analytically, our algorithm achieves perfect node-wise correspondence at the information-theoretic threshold—matching all nodes exactly under critical sparsity conditions.

This work proposes a universal graph foundation model designed to encode arbitrary graphs into vector representations that preserve both structural and semantic information, thereby supporting graph-level tasks and enabling cross-domain generalization. The approach integrates a multi-graph feature alignment mechanism with a density-maximized mean alignment algorithm to enhance consistency of node embeddings across datasets. Discriminative graph representations are learned through graph neural networks combined with contrastive learning, while a novel pooling-free, multi-layer reference distribution module efficiently aggregates node-level information into graph-level representations. Theoretical analysis provides an upper bound on the generalization error. Extensive experiments demonstrate that the model significantly outperforms strong baselines on few-shot graph classification and clustering tasks, validating its superior representational capacity and generalization ability.

This work addresses the challenge of accurately and efficiently establishing node correspondences in unsupervised graph alignment by proposing a novel "global representation and alignment" paradigm. Departing from the conventional decoupled framework of "local representation, global alignment," the method unifies representation learning and alignment into a single integrated process. It leverages a global attention mechanism combined with hierarchical cross-graph optimal transport to achieve anchor-free alignment. Furthermore, an efficient variant, GlobAlign-E, is introduced, reducing the computational complexity of optimal transport from cubic to quadratic. Experimental results demonstrate that the proposed approach improves alignment accuracy by up to 20% and accelerates computation by an order of magnitude compared to existing optimal transport-based methods, offering significant advantages in both precision and efficiency.

Existing GNN-based GED approximation methods suffer from two key limitations: (i) difficulty in modeling global structural correspondences, and (ii) spurious signals introduced by node-level matching, leading to inaccurate edit cost estimation. This paper proposes a decoupled graph similarity learning framework—the first to jointly model graph-level alignment and substructure-level edit cost estimation. It explicitly distinguishes aligned from unaligned substructures, thereby avoiding structural mismatches and cost confounding. An end-to-end GNN architecture enables global alignment-aware similarity estimation. The method achieves state-of-the-art performance on four benchmark datasets. Ablation studies and visualization analyses confirm that the model learns semantically coherent, well-decoupled substructure representations—significantly improving both GED approximation accuracy and interpretability.

This work addresses the problem of recovering the hidden vertex correspondence between two correlated graphs while jointly leveraging edge weights and node features. To this end, the authors introduce a correlated Gaussian Wigner model with node features, where both graph structure and features are coupled through an unknown permutation. The key contribution lies in the first systematic characterization of the information-theoretic limits of this alignment problem, accompanied by the development of QPAlign—an efficient algorithm grounded in quadratic programming relaxation that integrates statistical inference with optimization techniques and enjoys theoretical guarantees. Extensive experiments demonstrate that QPAlign achieves superior performance on both synthetic and real-world datasets, and theoretical analysis confirms its convergence and reliability.