# De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs

arXiv: https://arxiv.org/abs/2209.08311 · HTML: https://mlsanity.com/paper/2209.08311/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 17 Sep 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020)
- [Memory in network flows and its effects on spreading dynamics and community detection](https://mlsanity.com/paper/1305.4807/) (2013)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks](https://mlsanity.com/paper/1307.4030/) (2013)
- [Representing higher-order dependencies in networks](https://mlsanity.com/paper/1508.03113/) (2015)
- [When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks](https://mlsanity.com/paper/1702.05499/) (2017)
- [Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data](https://mlsanity.com/paper/2103.05031/) (2021)
- [Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities](https://mlsanity.com/paper/1508.06467/) (2015)
- [Directed Percolation in Temporal Networks](https://mlsanity.com/paper/2107.01510/) (2021)
- [HONEM: Learning Embedding for Higher Order Networks](https://mlsanity.com/paper/1908.05387/) (2019)
- [Using higher-order Markov models to reveal flow-based communities in networks](https://mlsanity.com/paper/1601.03516/) (2016)
- [Deep Ensembles for Graphs with Higher-order Dependencies](https://mlsanity.com/paper/2205.13988/) (2022)
- [Counting Causal Paths in Big Times Series Data on Networks](https://mlsanity.com/paper/1905.11287/) (2019)
- [Efficient limited-time reachability estimation in temporal networks](https://mlsanity.com/paper/1908.11831/) (2019)

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

- [Exploring Causal Learning through Graph Neural Networks: An In-depth Review](https://mlsanity.com/paper/2311.14994/) (2023)
- [Using Time-Aware Graph Neural Networks to Predict Temporal Centralities in Dynamic Graphs](https://mlsanity.com/paper/2310.15865/) (2023)
- [From Link Prediction to Forecasting: Addressing Challenges in Batch-based Temporal Graph Learning](https://mlsanity.com/paper/2406.04897/) (2024)
- [Weisfeiler and Leman Follow the Arrow of Time: Expressive Power of Message Passing in Temporal Event Graphs](https://mlsanity.com/paper/2505.24438/) (2025)
- [One Graph to Rule them All: Using NLP and Graph Neural Networks to analyse Tolkien's Legendarium](https://mlsanity.com/paper/2210.07871/) (2022)
- [Inference of Sequential Patterns for Neural Message Passing in Temporal Graphs](https://mlsanity.com/paper/2406.16552/) (2024)
- [Deep Graph Learning will stall without Network Science](https://mlsanity.com/paper/2502.01177/) (2025)
- [CLGNN: A Contrastive Learning-based GNN Model for Betweenness Centrality Prediction on Temporal Graphs](https://mlsanity.com/paper/2506.14122/) (2025)
- [Bridging the Divide: End-to-End Sequence-Graph Learning](https://mlsanity.com/paper/2510.25126/) (2025)
- [Do Temporal Link Predictors Need Learned Memory? A Smoothed-Count Baseline with a Handful of Parameters](https://mlsanity.com/paper/2609.35364/) (2026)

## Abstract (arXiv)

We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware graph neural network architecture for time-resolved data on dynamic graphs. Our approach accounts for temporal-topological patterns that unfold in the causal topology of dynamic graphs, which is determined by causal walks, i.e. temporally ordered sequences of links by which nodes can influence each other over time. Our architecture builds on multiple layers of higher-order De Bruijn graphs, an iterative line graph construction where nodes in a De Bruijn graph of order k represent walks of length k-1, while edges represent walks of length k. We develop a graph neural network architecture that utilizes De Bruijn graphs to implement a message passing scheme that follows a non-Markovian dynamics, which enables us to learn patterns in the causal topology of a dynamic graph. Addressing the issue that De Bruijn graphs with different orders k can be used to model the same data set, we further apply statistical model selection to determine the optimal graph topology to be used for message passing. An evaluation in synthetic and empirical data sets suggests that DBGNNs can leverage temporal patterns in dynamic graphs, which substantially improves the performance in a supervised node classification task.