# The eigenvalues of stochastic blockmodel graphs

arXiv: https://arxiv.org/abs/1803.11551 · HTML: https://mlsanity.com/paper/1803.11551/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2018.

## Built on by (most cited first, 7 of 7)

- [Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information](https://mlsanity.com/paper/2201.05923/) (2022)
- [Fast and Robust Sparsity-Aware Block Diagonal Representation](https://mlsanity.com/paper/2312.01137/) (2023)
- [Approximate Fr'echet Mean for Data Sets of Sparse Graphs](https://mlsanity.com/paper/2105.04062/) (2021)
- [Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms](https://mlsanity.com/paper/2202.04061/) (2022)
- [Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models](https://mlsanity.com/paper/2207.02168/) (2022)
- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)
- [Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities](https://mlsanity.com/paper/2603.05703/) (2026)

## Abstract (arXiv)

We derive the limiting distribution for the largest eigenvalues of the adjacency matrix for a stochastic blockmodel graph when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate normal with bounded covariances. Our result extends the classic result of F"uredi and Koml'os on the fluctuation of the largest eigenvalue for ErdHos-R'enyi graphs.