# Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model

arXiv: https://arxiv.org/abs/2601.06262 · HTML: https://mlsanity.com/paper/2601.06262/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [The ground truth about metadata and community detection in networks](https://mlsanity.com/paper/1608.05878/) (2016)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models](https://mlsanity.com/paper/1310.4378/) (2013)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Convexified Modularity Maximization for Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1512.08425/) (2015)
- [Learning a Latent Simplex in Input-Sparsity Time](https://mlsanity.com/paper/2105.08005/) (2021)
- [Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels](https://mlsanity.com/paper/2212.05053/) (2022)
- [Efficiently inferring community structure in bipartite networks](https://mlsanity.com/paper/1403.2933/) (2014)
- [Finding a latent k-simplex in O(k . nnz(data)) time via Subset Smoothing](https://mlsanity.com/paper/1904.06738/) (2019)
- [Normalized mutual information is a biased measure for classification and community detection](https://mlsanity.com/paper/2307.01282/) (2023)
- [Smoothed Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/2110.05528/) (2021)
- [Orthogonal symmetric non-negative matrix factorization under the stochastic block model](https://mlsanity.com/paper/1605.05349/) (2016)
- [Discovering overlapping communities in multi-layer directed networks](https://mlsanity.com/paper/2407.16152/) (2024)

## Built on by (most cited first, 1 of 1)

- [Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection](https://mlsanity.com/paper/2610.01361/) (2026)

## Abstract (arXiv)

Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an established model that accounts for the heterogeneity of node degrees. However, inference methods are computationally costly and highly sensitive to initialization, while cheaper alternatives, such as spectral or modularity-based approaches, are restricted to detecting specific structures, typically assortative. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem. Leveraging this insight, we propose a novel method for community detection and a theoretically well-grounded initialization strategy that provides an initial estimate of communities for inference algorithms. Our approach is agnostic to any specific network structure and applies to graphs with any structure representable by a DCBM. Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference while being faster; for instance, it processes a graph with 100,000 nodes and 1,000,000 edges in approximately 4 minutes. Moreover, the proposed initialization strategy significantly improves solution quality and reduces the number of iterations required by all tested inference algorithms. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.