# How Many Communities Are There?

arXiv: https://arxiv.org/abs/1412.1684 · HTML: https://mlsanity.com/paper/1412.1684/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2014.

## Built on by (most cited first, 8 of 8)

- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [Directed degree corrected mixed membership model and estimating community memberships in directed networks](https://mlsanity.com/paper/2109.07826/) (2021)
- [Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks](https://mlsanity.com/paper/2206.08465/) (2022)
- [Strongly Consistent Community Detection in Popularity Adjusted Block Models](https://mlsanity.com/paper/2506.07224/) (2025)
- [Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomalies](https://mlsanity.com/paper/2207.09324/) (2022)
- [Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models](https://mlsanity.com/paper/2406.05340/) (2024)
- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)
- [How many asymmetric communities are there in multi-layer directed networks?](https://mlsanity.com/paper/2602.21569/) (2026)

## Abstract (arXiv)

Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.