# Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models

arXiv: https://arxiv.org/abs/2406.05340 · HTML: https://mlsanity.com/paper/2406.05340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 8 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Exact Recovery in the Stochastic Block Model](https://mlsanity.com/paper/1405.3267/) (2014)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Minimax Rates of Community Detection in Stochastic Block Models](https://mlsanity.com/paper/1507.05313/) (2015)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Network Cross-Validation for Determining the Number of Communities in Network Data](https://mlsanity.com/paper/1411.1715/) (2014)
- [Community detection in sparse networks via Grothendieck's inequality](https://mlsanity.com/paper/1411.4686/) (2014)
- [Strong Consistency, Graph Laplacians, and the Stochastic Block Model](https://mlsanity.com/paper/2004.09780/) (2020)
- [A goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/1412.4857/) (2014)
- [Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection](https://mlsanity.com/paper/1710.11268/) (2017)
- [Robust and computationally feasible community detection in the presence of arbitrary outlier nodes](https://mlsanity.com/paper/1404.6000/) (2014)
- [Convexified Modularity Maximization for Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1512.08425/) (2015)
- [Hierarchical community detection by recursive partitioning](https://mlsanity.com/paper/1810.01509/) (2018)
- [Convex Relaxation Methods for Community Detection](https://mlsanity.com/paper/1810.00315/) (2018)
- [Determining the Number of Communities in Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1809.01028/) (2018)
- [Estimating the number of communities in a network](https://mlsanity.com/paper/1605.02753/) (2016)
- [Testing for Global Network Structure Using Small Subgraph Statistics](https://mlsanity.com/paper/1710.00862/) (2017)
- [How Many Communities Are There?](https://mlsanity.com/paper/1412.1684/) (2014)
- [Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models](https://mlsanity.com/paper/1703.06558/) (2017)
- [Optimal Adaptivity of Signed-Polygon Statistics for Network Testing](https://mlsanity.com/paper/1904.09532/) (2019)
- [A spectral method for community detection in moderately-sparse degree-corrected stochastic block models](https://mlsanity.com/paper/1506.08621/) (2015)
- [Network Global Testing by Counting Graphlets](https://mlsanity.com/paper/1807.08440/) (2018)
- [Consistency of Spectral Clustering on Hierarchical Stochastic Block Models](https://mlsanity.com/paper/2004.14531/) (2020)
- [Optimal Estimation of the Number of Communities](https://mlsanity.com/paper/2009.09177/) (2020)

## Abstract (arXiv)

We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled in the same way as in the standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selecting the number of communities is based on a sequential testing framework. In each step, the weighted DCSBM is fitted via some spectral clustering method. A key component of our method is matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the test statistic is then obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real-world network data demonstrate the desirable empirical properties of our method.