# Euclidean mirrors and dynamics in network time series

arXiv: https://arxiv.org/abs/2205.06877 · HTML: https://mlsanity.com/paper/2205.06877/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2022.

## Built on by (most cited first, 6 of 6)

- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [Signed Diverse Multiplex Networks: Clustering and Inference](https://mlsanity.com/paper/2402.10242/) (2024)
- [Control Charts for Multi-agent Systems](https://mlsanity.com/paper/2605.11135/) (2026)
- [Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings](https://mlsanity.com/paper/2409.17544/) (2024)
- [Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities](https://mlsanity.com/paper/2603.05703/) (2026)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)

## Abstract (arXiv)

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations, called Euclidean mirrors, permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.