# Higher-Order Spectral Clustering for Geometric Graphs

arXiv: https://arxiv.org/abs/2009.11353 · HTML: https://mlsanity.com/paper/2009.11353/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2020.

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

- [Spectral clustering in the Gaussian mixture block model](https://mlsanity.com/paper/2305.00979/) (2023)
- [On the Robustness of Spectral Algorithms for Semirandom Stochastic Block Models](https://mlsanity.com/paper/2412.14315/) (2024)
- [Multi-Community Spectral Clustering for Geometric Graphs](https://mlsanity.com/paper/2508.00893/) (2025)
- [Optimal Graph Clustering without Edge Density Signals](https://mlsanity.com/paper/2510.21669/) (2025)
- [Spectral graph clustering with inhomogeneous latent geometry](https://mlsanity.com/paper/2608.11321/) (2026)

## Abstract (arXiv)

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated with a higher-order eigenvalue. We establish the weak consistency of this algorithm for a wide class of geometric graphs which we call Soft Geometric Block Model. A small adjustment of the algorithm provides strong consistency. We also show that our method is effective in numerical experiments even for graphs of modest size.