# A spectral method for community detection in moderately-sparse degree-corrected stochastic block models

arXiv: https://arxiv.org/abs/1506.08621 · HTML: https://mlsanity.com/paper/1506.08621/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2015.

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

- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [A Comprehensive Review of Community Detection in Graphs](https://mlsanity.com/paper/2309.11798/) (2023)
- [Spectral clustering under degree heterogeneity: a case for the random walk Laplacian](https://mlsanity.com/paper/2105.00987/) (2021)
- [Enhancing ensemble learning and transfer learning in multimodal data analysis by adaptive dimensionality reduction](https://mlsanity.com/paper/2105.03682/) (2021)
- [Learning distributed representations with efficient SoftMax normalization](https://mlsanity.com/paper/2303.17475/) (2023)
- [Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models](https://mlsanity.com/paper/2207.02168/) (2022)
- [Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models](https://mlsanity.com/paper/2406.05340/) (2024)

## Abstract (arXiv)

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the block-membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log(n) or higher. Recovery succeeds even for very heterogeneous degree-distributions. The used algorithm does not rely on parameters as input. In particular, it does not need to know the number of communities.