# Spectral graph clustering with inhomogeneous latent geometry

arXiv: https://arxiv.org/abs/2608.11321 · HTML: https://mlsanity.com/paper/2608.11321/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Testing for high-dimensional geometry in random graphs](https://mlsanity.com/paper/1411.5713/) (2014)
- [Concentration and regularization of random graphs](https://mlsanity.com/paper/1506.00669/) (2015)
- [Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime](https://mlsanity.com/paper/2310.18280/) (2023)
- [Spectral clustering in the Gaussian mixture block model](https://mlsanity.com/paper/2305.00979/) (2023)
- [Community Detection on Euclidean Random Graphs](https://mlsanity.com/paper/1706.09942/) (2017)
- [The Geometric Block Model](https://mlsanity.com/paper/1709.05510/) (2017)
- [Higher-Order Spectral Clustering for Geometric Graphs](https://mlsanity.com/paper/2009.11353/) (2020)
- [Exact Community Recovery in the Geometric SBM](https://mlsanity.com/paper/2307.11196/) (2023)
- [Exact Label Recovery in Euclidean Random Graphs](https://mlsanity.com/paper/2407.11163/) (2024)
- [Community Recovery in the Geometric Block Model](https://mlsanity.com/paper/2206.11303/) (2022)
- [Sharp exact recovery threshold for two-community Euclidean random graphs](https://mlsanity.com/paper/2501.14830/) (2025)
- [Multi-Community Spectral Clustering for Geometric Graphs](https://mlsanity.com/paper/2508.00893/) (2025)

## Abstract (arXiv)

We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities. Nevertheless, we show in a block latent-space model that communities can be recovered from eigenvectors deeper in the spectrum. We analyze the spectral properties of the adjacency matrix through a limiting integral operator and use its structure to develop DBSPEC, a density-based spectral clustering algorithm that requires only approximate localization of the informative eigenvalue and is robust to poor eigenvalue separation. Crucially, this approach handles general latent geometries, overcoming restrictions to homogeneous toroidal models in prior works. Our theoretical predictions for the location of the informative eigenvalue notably align with observations in real-world experiments.