# Clustering Time-Evolving Networks Using the Spatio-Temporal Graph Laplacian

arXiv: https://arxiv.org/abs/2407.12864 · HTML: https://mlsanity.com/paper/2407.12864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 52 references that are in the map.
- First posted on arXiv 12 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [Kernel methods for detecting coherent structures in dynamical data](https://mlsanity.com/paper/1904.07752/) (2019)
- [Dynamical systems and complex networks: A Koopman operator perspective](https://mlsanity.com/paper/2405.08940/) (2024)
- [Community Discovery in Dynamic Networks: a Survey](https://mlsanity.com/paper/1707.03186/) (2017)
- [Spectral properties of the Laplacian of multiplex networks](https://mlsanity.com/paper/1307.2090/) (2013)
- [Koopman-based spectral clustering of directed and time-evolving graphs](https://mlsanity.com/paper/2204.02951/) (2022)
- [Evaluating Community Detection Algorithms for Progressively Evolving Graphs](https://mlsanity.com/paper/2007.08635/) (2020)
- [Transfer operators on graphs: Spectral clustering and beyond](https://mlsanity.com/paper/2305.11766/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)

## Abstract (arXiv)

Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis (CCA) to capture the temporal evolution of clusters. Based on this extended canonical correlation framework, we define the spatio-temporal graph Laplacian and investigate its spectral properties. We connect these concepts to dynamical systems theory via transfer operators, and illustrate the advantages of our method on benchmark graphs by comparison with existing methods. We show that the spatio-temporal graph Laplacian allows for a clear interpretation of cluster structure evolution over time for directed and undirected graphs.