# Mutual Information in Community Detection with Covariate Information and Correlated Networks

arXiv: https://arxiv.org/abs/1912.05375 · HTML: https://mlsanity.com/paper/1912.05375/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Correlated Stochastic Block Models: Exact Graph Matching with Applications to Recovering Communities](https://mlsanity.com/paper/2107.06767/) (2021)
- [Exact Recovery in the General Hypergraph Stochastic Block Model](https://mlsanity.com/paper/2105.04770/) (2021)
- [Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticity](https://mlsanity.com/paper/2106.11950/) (2021)
- [Exact Community Recovery in Correlated Stochastic Block Models](https://mlsanity.com/paper/2203.15736/) (2022)
- [Approximate Message Passing for the Matrix Tensor Product Model](https://mlsanity.com/paper/2306.15580/) (2023)
- [Community Detection in Weighted Multilayer Networks with Ambient Noise](https://mlsanity.com/paper/2103.00486/) (2021)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)

## Abstract (arXiv)

We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a heuristic analysis of a multivariate performance measure called the MMSE matrix. These results show that the combined effects of seemingly very different types of information can be characterized explicitly in terms of formulas involving low-dimensional estimation problems in additive Gaussian noise. Our analysis is supported by numerical simulations.