# Efficient Graph Matching for Correlated Stochastic Block Models

arXiv: https://arxiv.org/abs/2412.02661 · HTML: https://mlsanity.com/paper/2412.02661/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 71 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Exact alignment recovery for correlated ErdHos-R'enyi graphs](https://mlsanity.com/paper/1711.06783/) (2017)
- [Low-Degree Hardness of Detection for Correlated ErdHos-R'enyi Graphs](https://mlsanity.com/paper/2311.15931/) (2023)
- [A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation](https://mlsanity.com/paper/2306.00266/) (2023)
- [Fundamental limits of community detection from multi-view data: multi-layer, dynamic and partially labeled block models](https://mlsanity.com/paper/2401.08167/) (2024)
- [A computational transition for detecting correlated stochastic block models by low-degree polynomials](https://mlsanity.com/paper/2409.00966/) (2024)
- [Efficiently matching random inhomogeneous graphs via degree profiles](https://mlsanity.com/paper/2310.10441/) (2023)
- [Faster algorithms for the alignment of sparse correlated Erd"os-R'enyi random graphs](https://mlsanity.com/paper/2405.08421/) (2024)

## Built on by (most cited first, 5 of 5)

- [Computational Lower Bounds for Correlated Random Graphs via Algorithmic Contiguity](https://mlsanity.com/paper/2502.09832/) (2025)
- [Exact Matching in Correlated Networks with Node Attributes for Improved Community Recovery](https://mlsanity.com/paper/2501.02851/) (2025)
- [Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithm](https://mlsanity.com/paper/2412.16457/) (2024)
- [Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models](https://mlsanity.com/paper/2505.22935/) (2025)
- [Query-Limited Community Recovery in Stochastic Block Models](https://mlsanity.com/paper/2606.02055/) (2026)

## Abstract (arXiv)

We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree is logarithmic in the number of vertices, this algorithm correctly matches all but a vanishing fraction of vertices with high probability, whenever the edge correlation parameter s satisfies s2 > α ≈ 0.338, where α is Otter's tree-counting constant. Moreover, we extend this to an efficient algorithm for exact graph matching whenever this is information-theoretically possible, positively resolving an open problem of R'acz and Sridhar (NeurIPS 2021). Our algorithm generalizes the recent breakthrough work of Mao, Wu, Xu, and Yu (STOC 2023), which is based on centered subgraph counts of a large family of trees termed chandeliers. A major technical challenge that we overcome is dealing with the additional estimation errors that are necessarily present due to the fact that, in relevant parameter regimes, the latent community partition cannot be exactly recovered from a single graph. As an application of our results, we give an efficient algorithm for exact community recovery using multiple correlated graphs in parameter regimes where it is information-theoretically impossible to do so using just a single graph.