# Efficiently matching random inhomogeneous graphs via degree profiles

arXiv: https://arxiv.org/abs/2310.10441 · HTML: https://mlsanity.com/paper/2310.10441/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 30 of 32)

- [Efficient random graph matching via degree profiles](https://mlsanity.com/paper/1811.07821/) (2018)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [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)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [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)
- [Spectral Graph Matching and Regularized Quadratic Relaxations II: ErdHos-R'enyi Graphs and Universality](https://mlsanity.com/paper/1907.08883/) (2019)
- [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)
- [Random graph matching at Otter's threshold via counting chandeliers](https://mlsanity.com/paper/2209.12313/) (2022)
- [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)
- [Impossibility of Partial Recovery in the Graph Alignment Problem](https://mlsanity.com/paper/2102.02685/) (2021)
- [Seeded graph matching for correlated ErdHos-R'enyi graphs](https://mlsanity.com/paper/1304.7844/) (2013)
- [Convexified Modularity Maximization for Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1512.08425/) (2015)
- [Matching recovery threshold for correlated random graphs](https://mlsanity.com/paper/2205.14650/) (2022)
- [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)
- [Statistical limits of correlation detection in trees](https://mlsanity.com/paper/2209.13723/) (2022)
- [Seedless Graph Matching via Tail of Degree Distribution for Correlated Erdos-Renyi Graphs](https://mlsanity.com/paper/1907.06334/) (2019)
- [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)
- [The Power of D-hops in Matching Power-Law Graphs](https://mlsanity.com/paper/2102.12975/) (2021)
- [Matching Correlated Inhomogeneous Random Graphs using the k-core Estimator](https://mlsanity.com/paper/2302.05407/) (2023)

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

- [The Umeyama algorithm for matching correlated Gaussian geometric models in the low-dimensional regime](https://mlsanity.com/paper/2402.15095/) (2024)
- [Efficient Graph Matching for Correlated Stochastic Block Models](https://mlsanity.com/paper/2412.02661/) (2024)
- [Robust Point Matching with Distance Profiles](https://mlsanity.com/paper/2312.12641/) (2023)
- [Information-Theoretic Thresholds for the Alignments of Partially Correlated Graphs](https://mlsanity.com/paper/2406.05428/) (2024)
- [Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithm](https://mlsanity.com/paper/2412.16457/) (2024)

## Abstract (arXiv)

In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending the matching algorithm via degree profiles by Ding, Ma, Wu and Xu (2021), we obtain an efficient matching algorithm as long as the minimal average degree is at least Omega(log2 n) and the minimal correlation is at least 1 - O(log-2 n).