# General Community Detection with Optimal Recovery Conditions for Multi-relational Sparse Networks with Dependent Layers

arXiv: https://arxiv.org/abs/2004.03480 · HTML: https://mlsanity.com/paper/2004.03480/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2020.

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

- [ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network](https://mlsanity.com/paper/2102.10226/) (2021)
- [Fundamental limits of community detection from multi-view data: multi-layer, dynamic and partially labeled block models](https://mlsanity.com/paper/2401.08167/) (2024)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Fundamental Limits of Community Detection in Contextual Multi-Layer Stochastic Block Models](https://mlsanity.com/paper/2602.08173/) (2026)
- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [Algorithmic Contiguity from Low-Degree Heuristic II: Predicting Detection-Recovery Gaps](https://mlsanity.com/paper/2604.17410/) (2026)

## Abstract (arXiv)

Multilayer and multiplex networks are becoming common network data sets in recent times. We consider the problem of identifying the common community structure for a special type of multilayer networks called multi-relational networks. We consider extensions of the spectral clustering methods for multi-relational networks and give theoretical guarantees that the spectral clustering methods recover community structure consistently for multi-relational networks generated from multilayer versions of both stochastic and degree-corrected block models even with dependence between network layers. The methods are shown to work under optimal conditions on the degree parameter of the networks to detect both assortative and disassortative community structures with vanishing error proportions even if individual layers of the multi-relational network has the network structures below community detectability threshold. We reinforce the validity of the theoretical results via simulations too.