# Estimating the number of communities in a network

arXiv: https://arxiv.org/abs/1605.02753 · HTML: https://mlsanity.com/paper/1605.02753/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2016.

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

- [Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths](https://mlsanity.com/paper/2112.00183/) (2021)
- [Directed degree corrected mixed membership model and estimating community memberships in directed networks](https://mlsanity.com/paper/2109.07826/) (2021)
- [Fast sampling and model selection for Bayesian mixture models](https://mlsanity.com/paper/2501.07668/) (2025)
- [Estimating the number of clusters of a Block Markov Chain](https://mlsanity.com/paper/2407.18287/) (2024)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models](https://mlsanity.com/paper/2406.05340/) (2024)
- [Mixture models for data with unknown distributions](https://mlsanity.com/paper/2502.19605/) (2025)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Natural Language Processing Psychometrics](https://mlsanity.com/paper/2608.07316/) (2026)

## Abstract (arXiv)

Community detection, the division of a network into dense subnetworks with only sparse connections between them, has been a topic of vigorous study in recent years. However, while there exist a range of powerful and flexible methods for dividing a network into a specified number of communities, it is an open question how to determine exactly how many communities one should use. Here we describe a mathematically principled approach for finding the number of communities in a network using a maximum-likelihood method. We demonstrate the approach on a range of real-world examples with known community structure, finding that it is able to determine the number of communities correctly in every case.