# Space-Time Graph Neural Networks

arXiv: https://arxiv.org/abs/2110.02880 · HTML: https://mlsanity.com/paper/2110.02880/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 30)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Graph Neural Networks for Decentralized Multi-Robot Path Planning](https://mlsanity.com/paper/1912.06095/) (2019)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Graph Convolutional Neural Networks via Scattering](https://mlsanity.com/paper/1804.00099/) (2018)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [Recurrent Space-time Graph Neural Networks](https://mlsanity.com/paper/1904.05582/) (2019)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [Graph and graphon neural network stability](https://mlsanity.com/paper/2010.12529/) (2020)
- [Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learning](https://mlsanity.com/paper/2012.14906/) (2020)
- [BridgeDPI: A Novel Graph Neural Network for Predicting Drug-Protein Interactions](https://mlsanity.com/paper/2101.12547/) (2021)
- [Distributed Linear-Quadratic Control with Graph Neural Networks](https://mlsanity.com/paper/2103.08417/) (2021)
- [Graph-Time Convolutional Neural Networks](https://mlsanity.com/paper/2103.01730/) (2021)
- [Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control](https://mlsanity.com/paper/2104.13868/) (2021)
- [Unsupervised Resource Allocation with Graph Neural Networks](https://mlsanity.com/paper/2106.09761/) (2021)
- [Continuous-Depth Neural Models for Dynamic Graph Prediction](https://mlsanity.com/paper/2106.11581/) (2021)

## Built on by (most cited first, 10 of 10)

- [Spatio-Temporal Graph Neural Networks: A Survey](https://mlsanity.com/paper/2301.10569/) (2023)
- [Training Stable Graph Neural Networks Through Constrained Learning](https://mlsanity.com/paper/2110.03576/) (2021)
- [Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis](https://mlsanity.com/paper/2206.15174/) (2022)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Space-Time Graph Neural Networks with Stochastic Graph Perturbations](https://mlsanity.com/paper/2210.16270/) (2022)
- [Representation Power of Graph Neural Networks: Improved Expressivity via Algebraic Analysis](https://mlsanity.com/paper/2205.09801/) (2022)
- [Edge-Varying Fourier Graph Networks for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2210.03093/) (2022)
- [Unrolled Graph Neural Networks for Constrained Optimization](https://mlsanity.com/paper/2509.17156/) (2025)
- [Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?](https://mlsanity.com/paper/2402.03558/) (2024)

## Abstract (arXiv)

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators. We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.