# A Simple and Powerful Framework for Stable Dynamic Network Embedding

arXiv: https://arxiv.org/abs/2311.09251 · HTML: https://mlsanity.com/paper/2311.09251/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Node Embedding over Temporal Graphs](https://mlsanity.com/paper/1903.08889/) (2019)
- [dynnode2vec: Scalable Dynamic Network Embedding](https://mlsanity.com/paper/1812.02356/) (2018)
- [Dynamic stochastic blockmodels for time-evolving social networks](https://mlsanity.com/paper/1403.0921/) (2014)
- [The multilayer random dot product graph](https://mlsanity.com/paper/2007.10455/) (2020)
- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [GloDyNE: Global Topology Preserving Dynamic Network Embedding](https://mlsanity.com/paper/2008.01935/) (2020)

## Built on by (most cited first, 5 of 5)

- [Learning Invariant Representations of Graph Neural Networks via Cluster Generalization](https://mlsanity.com/paper/2403.03599/) (2024)
- [Valid Conformal Prediction for Dynamic GNNs](https://mlsanity.com/paper/2405.19230/) (2024)
- [Valid Bootstraps for Network Embeddings with Applications to Network Visualisation](https://mlsanity.com/paper/2410.20895/) (2024)
- [Unsupervised Attributed Dynamic Network Embedding with Stability Guarantees](https://mlsanity.com/paper/2503.02859/) (2025)
- [Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation](https://mlsanity.com/paper/2508.12674/) (2025)

## Abstract (arXiv)

In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and established, the field of dynamic network embedding is comparatively in its infancy. We propose that a wide class of established static network embedding methods can be used to produce interpretable and powerful dynamic network embeddings when they are applied to the dilated unfolded adjacency matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space. We additionally define a hypothesis testing framework which can be used to evaluate the quality of a dynamic network embedding by testing for planted structure in simulated networks. Using this, we demonstrate that, even in trivial cases, unstable methods are often either conservative or encode incorrect structure. In contrast, we demonstrate that our suite of stable unfolded methods are not only more interpretable but also more powerful in comparison to their unstable counterparts.