# Spectral Clustering for Multiple Sparse Networks: I

arXiv: https://arxiv.org/abs/1805.10594 · HTML: https://mlsanity.com/paper/1805.10594/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2018.

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

- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Consensus Knowledge Graph Learning via Multi-view Sparse Low Rank Block Model](https://mlsanity.com/paper/2209.13762/) (2022)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [A pseudo-likelihood approach to community detection in weighted networks](https://mlsanity.com/paper/2303.05909/) (2023)
- [Privacy-Preserving Community Detection for Locally Distributed Multiple Networks](https://mlsanity.com/paper/2306.15709/) (2023)
- [Bias-Corrected Joint Spectral Embedding for Multilayer Networks with Invariant Subspace: Entrywise Eigenvector Perturbation and Inference](https://mlsanity.com/paper/2406.07849/) (2024)

## Abstract (arXiv)

Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of connection between each other are known as multiple or multi-layer networks. We consider the problem of identifying the common community structures for multiple networks. We consider extensions of the spectral clustering methods for the multiple sparse networks, and give theoretical guarantee that the spectral clustering methods produce consistent community detection in case of both multiple stochastic block model and multiple degree-corrected block models. The methods are shown to work under sufficiently mild conditions on the number of multiple networks to detect associative community structures, even if all the individual networks are sparse and most of the individual networks are below community detectability threshold. We reinforce the validity of the theoretical results via simulations too.