# Tracking Network Dynamics using Probabilistic State-Space Models

arXiv: https://arxiv.org/abs/2409.08238 · HTML: https://mlsanity.com/paper/2409.08238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2024.

## Built on by (most cited first, 3 of 3)

- [A Few Moments Please: Scalable Graphon Learning via Moment Matching](https://mlsanity.com/paper/2506.04206/) (2025)
- [Toward a Graph-Theoretic Model of Belief: Confidence, Credibility, and Structural Coherence](https://mlsanity.com/paper/2508.03465/) (2025)
- [Topological Kalman Filtering on Cell Complexes](https://mlsanity.com/paper/2605.15955/) (2026)

## Abstract (arXiv)

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise estimates, our method accounts for dynamic changes in the network structure over time. We model the network at each timestep as the state of the SSM, and use observations to update beliefs that quantify the probability of the network being in a particular state. Then, by considering the dynamics of transition and observation models through the update and prediction steps, respectively, the proposed method can incorporate the information of real-time graph signals into the beliefs. These beliefs provide a probability distribution of the network at each timestep, being able to provide both an estimate for the network and the uncertainty it entails. Our approach is evaluated through experiments with synthetic and real-world networks. The results demonstrate that our method effectively estimates network states and accounts for the uncertainty in the data, outperforming traditional techniques such as recursive least squares.