# Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodel

arXiv: https://arxiv.org/abs/2011.04558 · HTML: https://mlsanity.com/paper/2011.04558/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Spectral clustering under degree heterogeneity: a case for the random walk Laplacian](https://mlsanity.com/paper/2105.00987/) (2021)
- [Matrix factorisation and the interpretation of geodesic distance](https://mlsanity.com/paper/2106.01260/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labels](https://mlsanity.com/paper/2208.08638/) (2022)
- [Depth-Based Local Center Clustering: A Framework for Handling Different Clustering Scenarios](https://mlsanity.com/paper/2505.09516/) (2025)
- [Latent structure blockmodels for Bayesian spectral graph clustering](https://mlsanity.com/paper/2107.01734/) (2021)
- [Unsupervised Attributed Dynamic Network Embedding with Stability Guarantees](https://mlsanity.com/paper/2503.02859/) (2025)
- [Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding](https://mlsanity.com/paper/2603.11965/) (2026)

## Abstract (arXiv)

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition of the matrix. Estimating correctly the number of communities and the dimension of the reduced latent space is critical for good performance of spectral clustering algorithms. Furthermore, many real-world graphs, such as enterprise computer networks studied in cyber-security applications, often display heterogeneous within-community degree distributions. Such heterogeneous degree distributions are usually not well captured by standard spectral clustering algorithms. In this article, a novel spectral clustering algorithm is proposed for community detection under the degree-corrected stochastic blockmodel. The proposed method is based on a transformation of the spectral embedding to spherical coordinates, and a novel modelling assumption in the transformed space. The method allows for simultaneous and automated selection of the number of communities and the latent dimension for spectral embeddings of graphs with uneven node degrees. Results show improved performance over competing methods in representing computer networks.