# Graph Matching via Optimal Transport

arXiv: https://arxiv.org/abs/2111.05366 · HTML: https://mlsanity.com/paper/2111.05366/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [GraSPy: Graph Statistics in Python](https://mlsanity.com/paper/1904.05329/) (2019)
- [Spectral Clustering for Divide-and-Conquer Graph Matching](https://mlsanity.com/paper/1310.1297/) (2013)
- [Vertex Nomination Via Seeded Graph Matching](https://mlsanity.com/paper/1705.00674/) (2017)

## Built on by (most cited first, 6 of 6)

- [Joint Optimal Transport and Embedding for Network Alignment](https://mlsanity.com/paper/2502.19334/) (2025)
- [Bilingual Lexicon Induction for Low-Resource Languages using Graph Matching via Optimal Transport](https://mlsanity.com/paper/2210.14378/) (2022)
- [Double-Bounded Optimal Transport for Advanced Clustering and Classification](https://mlsanity.com/paper/2401.11418/) (2024)
- [Multiscale Graph Comparison via the Embedded Laplacian Discrepancy](https://mlsanity.com/paper/2201.12064/) (2022)
- [Deep Semantic Graph Matching for Large-scale Outdoor Point Clouds Registration](https://mlsanity.com/paper/2308.05314/) (2023)
- [Scalable Optimal Transport Algorithm for Network Alignment](https://mlsanity.com/paper/2607.11952/) (2026)

## Abstract (arXiv)

The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations research, computer vision, neuroscience, and more. However, current state-of-the-art algorithms are inefficient in matching very large graphs, though they produce good accuracy. The main computational bottleneck of these algorithms is the linear assignment problem, which must be solved at each iteration. In this paper, we leverage the recent advances in the field of optimal transport to replace the accepted use of linear assignment algorithms. We present GOAT, a modification to the state-of-the-art graph matching approximation algorithm "FAQ" (Vogelstein, 2015), replacing its linear sum assignment step with the "Lightspeed Optimal Transport" method of Cuturi (2013). The modification provides improvements to both speed and empirical matching accuracy. The effectiveness of the approach is demonstrated in matching graphs in simulated and real data examples.