# Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

arXiv: https://arxiv.org/abs/1708.02620 · HTML: https://mlsanity.com/paper/1708.02620/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2017.

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

- [Multilayer Graph Contrastive Clustering Network](https://mlsanity.com/paper/2112.14021/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Spectral Clustering of Attributed Multi-relational Graphs](https://mlsanity.com/paper/2311.01840/) (2023)
- [Multilayer Graph Clustering with Optimized Node Embedding](https://mlsanity.com/paper/2103.16534/) (2021)
- [Information Fusion: Scaling Subspace-Driven Approaches](https://mlsanity.com/paper/2204.12035/) (2022)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)
- [Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection](https://mlsanity.com/paper/2610.01361/) (2026)

## Abstract (arXiv)

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal plus noise model, we provide a phase transition analysis of clustering reliability. Moreover, we use the phase transition criterion to propose a multilayer iterative model order selection algorithm (MIMOSA) for multilayer SGC, which features automated cluster assignment and layer weight adaptation, and provides statistical clustering reliability guarantees. Numerical simulations on synthetic multilayer graphs verify the phase transition analysis, and experiments on real-world multilayer graphs show that MIMOSA is competitive or better than other clustering methods.