# Matching recovery threshold for correlated random graphs

arXiv: https://arxiv.org/abs/2205.14650 · HTML: https://mlsanity.com/paper/2205.14650/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 29 May 2022.

## Builds on (most cited first, 20 of 20)

- [Efficient random graph matching via degree profiles](https://mlsanity.com/paper/1811.07821/) (2018)
- [Settling the Sharp Reconstruction Thresholds of Random Graph Matching](https://mlsanity.com/paper/2102.00082/) (2021)
- [Exact alignment recovery for correlated ErdHos-R'enyi graphs](https://mlsanity.com/paper/1711.06783/) (2017)
- [Improved Achievability and Converse Bounds for ErdHos-R'enyi Graph Matching](https://mlsanity.com/paper/1602.01042/) (2016)
- [(Nearly) Efficient Algorithms for the Graph Matching Problem on Correlated Random Graphs](https://mlsanity.com/paper/1805.02349/) (2018)
- [Seeded Graph Matching via Large Neighborhood Statistics](https://mlsanity.com/paper/1807.10262/) (2018)
- [Partial Recovery in the Graph Alignment Problem](https://mlsanity.com/paper/2007.00533/) (2020)
- [From tree matching to sparse graph alignment](https://mlsanity.com/paper/2002.01258/) (2020)
- [Testing correlation of unlabeled random graphs](https://mlsanity.com/paper/2008.10097/) (2020)
- [Partial Recovery of ErdHos-R'enyi Graph Alignment via k-Core Alignment](https://mlsanity.com/paper/1809.03553/) (2018)
- [Exact Matching of Random Graphs with Constant Correlation](https://mlsanity.com/paper/2110.05000/) (2021)
- [Correlated Stochastic Block Models: Exact Graph Matching with Applications to Recovering Communities](https://mlsanity.com/paper/2107.06767/) (2021)
- [Testing network correlation efficiently via counting trees](https://mlsanity.com/paper/2110.11816/) (2021)
- [Random Graph Matching in Geometric Models: the Case of Complete Graphs](https://mlsanity.com/paper/2202.10662/) (2022)
- [Seeded graph matching for correlated ErdHos-R'enyi graphs](https://mlsanity.com/paper/1304.7844/) (2013)
- [Detection threshold for correlated ErdHos-R'enyi graphs via densest subgraphs](https://mlsanity.com/paper/2203.14573/) (2022)
- [Correlated randomly growing graphs](https://mlsanity.com/paper/2004.13537/) (2020)
- [Seedless Graph Matching via Tail of Degree Distribution for Correlated Erdos-Renyi Graphs](https://mlsanity.com/paper/1907.06334/) (2019)
- [The planted matching problem: Sharp threshold and infinite-order phase transition](https://mlsanity.com/paper/2103.09383/) (2021)
- [One-Way Matching of Datasets with Low Rank Signals](https://mlsanity.com/paper/2204.13858/) (2022)

## Built on by (most cited first, 16 of 16)

- [Random graph matching at Otter's threshold via counting chandeliers](https://mlsanity.com/paper/2209.12313/) (2022)
- [Statistical limits of correlation detection in trees](https://mlsanity.com/paper/2209.13723/) (2022)
- [A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation](https://mlsanity.com/paper/2306.00266/) (2023)
- [A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation](https://mlsanity.com/paper/2212.13677/) (2022)
- [Matching Correlated Inhomogeneous Random Graphs using the k-core Estimator](https://mlsanity.com/paper/2302.05407/) (2023)
- [The Umeyama algorithm for matching correlated Gaussian geometric models in the low-dimensional regime](https://mlsanity.com/paper/2402.15095/) (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)
- [Computational Lower Bounds for Correlated Random Graphs via Algorithmic Contiguity](https://mlsanity.com/paper/2502.09832/) (2025)
- [The feasibility of multi-graph alignment: a Bayesian approach](https://mlsanity.com/paper/2502.17142/) (2025)
- [Perfect Recovery for Random Geometric Graph Matching with Shallow Graph Neural Networks](https://mlsanity.com/paper/2402.07340/) (2024)
- [Information-Theoretic Thresholds for the Alignments of Partially Correlated Graphs](https://mlsanity.com/paper/2406.05428/) (2024)
- [Testing Dependency of Weighted Random Graphs](https://mlsanity.com/paper/2409.14870/) (2024)
- [Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithm](https://mlsanity.com/paper/2412.16457/) (2024)
- [Chaining 2-FWL GNNs for Combinatorial Graph Alignment](https://mlsanity.com/paper/2510.03086/) (2025)
- [Auditing Bayesian Graph Alignment: Diagnostic Comparisons and Reference Failure](https://mlsanity.com/paper/2609.23232/) (2026)

## Abstract (arXiv)

For two correlated graphs which are independently sub-sampled from a common ErdHos-R'enyi graph G(n, p), we wish to recover their latent vertex matching from the observation of these two graphs without labels. When p = n-α+o(1) for α∈ (0, 1], we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.