# Multiscale dynamical embeddings of complex networks

arXiv: https://arxiv.org/abs/1804.03733 · HTML: https://mlsanity.com/paper/1804.03733/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

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

- [POLE: Polarized Embedding for Signed Networks](https://mlsanity.com/paper/2110.09899/) (2021)
- [A Broader Picture of Random-walk Based Graph Embedding](https://mlsanity.com/paper/2110.12344/) (2021)
- [Generalized Dirichlet Energy and Graph Laplacians for Clustering Directed and Undirected Graphs](https://mlsanity.com/paper/2203.03221/) (2022)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection](https://mlsanity.com/paper/2112.04388/) (2021)
- [The Hyperspherical Geometry of Community Detection: Modularity as a Distance](https://mlsanity.com/paper/2107.02645/) (2021)
- [Robust Markov stability for community detection at a scale learned based on the structure](https://mlsanity.com/paper/2504.11621/) (2025)
- [Embedding networks with the random walk first return time distribution](https://mlsanity.com/paper/2512.02694/) (2025)

## Abstract (arXiv)

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from Control Theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i)~dimensionality reduction, i.e., projecting nodes onto a low dimensional space that captures dynamic similarity at different time scales, and (ii)~how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity, and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to Control Theory, by using the here developed dynamical perspective.