Graph Alignment for Benchmarking Graph Neural Networks and Learning Positional Encodings

Adrien Lagesse; Marc Lelarge

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arXiv · 2505.13087

Graph Alignment for Benchmarking Graph Neural Networks and Learning Positional Encodings

Adrien Lagesse·Marc Lelarge

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Abstract

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping edges. We frame this problem as a self-supervised learning task and present several methods to generate graph alignment datasets using synthetic random graphs and real-world graph datasets from multiple domains. For a given graph dataset, we generate a family of graph alignment datasets with increasing difficulty, allowing us to rank the performance of various architectures. Our experiments prove that there is an optimal task difficulty for having a statistically relevant ranking of different models and that, even on a structure-only task, anisotropic models perform better compared to isotropic ones. To further prove that our synthetic task capture meaningful information, we show its effectiveness for self-supervised GNN pre-training: the learned node embeddings can be leveraged as positional encodings by transformers for graph regression or can be used to reconstruct the full structure of the graph with $98\%$ accuracy. To support reproducibility and further research, we provide an open-source Python package to generate graph alignment datasets and benchmark new GNN architectures. The source code is available at https://github.com/adrien-lagesse/graph-alignment-benchmark.

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BibTeX RIS

Adrien Lagesse, Marc Lelarge. 2026-06-22. Graph Alignment for Benchmarking Graph Neural Networks and Learning Positional Encodings. https://arxiv.org/abs/2505.13087

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