# Bayesian community detection for networks with covariates

arXiv: https://arxiv.org/abs/2203.02090 · HTML: https://mlsanity.com/paper/2203.02090/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015)
- [Covariate-assisted spectral clustering](https://mlsanity.com/paper/1411.2158/) (2014)
- [Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction](https://mlsanity.com/paper/1501.06218/) (2015)
- [On semidefinite relaxations for the block model](https://mlsanity.com/paper/1406.5647/) (2014)
- [Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares](https://mlsanity.com/paper/1705.02973/) (2017)
- [Multiway clustering via tensor block models](https://mlsanity.com/paper/1906.03807/) (2019)
- [Covariate Regularized Community Detection in Sparse Graphs](https://mlsanity.com/paper/1607.02675/) (2016)
- [Community Detection in Networks with Node Features](https://mlsanity.com/paper/1509.01173/) (2015)
- [Leveraging Node Attributes for Incomplete Relational Data](https://mlsanity.com/paper/1706.04289/) (2017)
- [Community detection with nodal information](https://mlsanity.com/paper/1610.09735/) (2016)
- [Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks](https://mlsanity.com/paper/1904.05330/) (2019)
- [Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models](https://mlsanity.com/paper/2009.12267/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Comprehensive Review of Community Detection in Graphs](https://mlsanity.com/paper/2309.11798/) (2023)
- [Network two-sample test for block models](https://mlsanity.com/paper/2406.06014/) (2024)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Clustering with Uniformity- and Neighbor-Based Random Geometric Graphs](https://mlsanity.com/paper/2501.06268/) (2025)

## Abstract (arXiv)

The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms. Among the various learning tasks with network data, community detection, the discovery of node clusters or "communities," has arguably received the most attention in the scientific community. In many real-world applications, the network data often come with additional information in the form of node or edge covariates that should ideally be leveraged for inference. In this paper, we add to a limited literature on community detection for networks with covariates by proposing a Bayesian stochastic block model with a covariate-dependent random partition prior. Under our prior, the covariates are explicitly expressed in specifying the prior distribution on the cluster membership. Our model has the flexibility of modeling uncertainties of all the parameter estimates including the community membership. Importantly, and unlike the majority of existing methods, our model has the ability to learn the number of the communities via posterior inference without having to assume it to be known. Our model can be applied to community detection in both dense and sparse networks, with both categorical and continuous covariates, and our MCMC algorithm is very efficient with good mixing properties. We demonstrate the superior performance of our model over existing models in a comprehensive simulation study and an application to two real datasets.