# Global and Individualized Community Detection in Inhomogeneous Multilayer Networks

arXiv: https://arxiv.org/abs/2012.00933 · HTML: https://mlsanity.com/paper/2012.00933/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 11 of 11)

- [Exact Community Recovery in Correlated Stochastic Block Models](https://mlsanity.com/paper/2203.15736/) (2022)
- [Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA](https://mlsanity.com/paper/2303.06198/) (2023)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model](https://mlsanity.com/paper/2207.04600/) (2022)
- [Optimal and exact recovery on the general nonuniform Hypergraph Stochastic Block Model](https://mlsanity.com/paper/2304.13139/) (2023)
- [Information-Theoretic Limits and Strong Consistency on Binary Non-uniform Hypergraph Stochastic Block Models](https://mlsanity.com/paper/2306.06845/) (2023)
- [Fundamental Limits of Community Detection in Contextual Multi-Layer Stochastic Block Models](https://mlsanity.com/paper/2602.08173/) (2026)
- [rMultiNet: An R Package For Multilayer Networks Analysis](https://mlsanity.com/paper/2302.04437/) (2023)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Community Detection in the Multi-View Stochastic Block Model](https://mlsanity.com/paper/2401.09510/) (2024)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)

## Abstract (arXiv)

In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multilayer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a stylized yet informative inhomogeneous multilayer network model. In our model, layers are generated by different stochastic block models, the community structures of which are (random) perturbations of a common global structure while the connecting probabilities in different layers are not related. Focusing on the symmetric two block case, we establish minimax rates for both global estimation of the common structure and individualized estimation of layer-wise community structures. Both minimax rates have sharp exponents. In addition, we provide an efficient algorithm that is simultaneously asymptotic minimax optimal for both estimation tasks under mild conditions. The optimal rates depend on the parity of the number of most informative layers, a phenomenon that is caused by inhomogeneity across layers. The method is extended to handle multiple and potentially asymmetric community cases. We demonstrate its effectiveness on both simulated examples and a real multi-modal single-cell dataset.