# Correlations of network trajectories

arXiv: https://arxiv.org/abs/2206.03334 · HTML: https://mlsanity.com/paper/2206.03334/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2022.

## Built on by (most cited first, 4 of 4)

- [Dynamical stability and chaos in artificial neural network trajectories along training](https://mlsanity.com/paper/2404.05782/) (2024)
- [Towards certification: A complete statistical validation pipeline for supervised learning in industry](https://mlsanity.com/paper/2411.02075/) (2024)
- [Leveraging chaotic transients in the training of artificial neural networks](https://mlsanity.com/paper/2506.08523/) (2025)
- [Scalar Representations of Neural Network Training Dynamics](https://mlsanity.com/paper/2606.30384/) (2026)

## Abstract (arXiv)

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlations function to the case of sequences of network snapshots, i.e. a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and illustrate how these patterns are revealed in empirical networks arising in different domains.