# Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs

arXiv: https://arxiv.org/abs/2408.09123 · HTML: https://mlsanity.com/paper/2408.09123/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 17 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [ROLAND: Graph Learning Framework for Dynamic Graphs](https://mlsanity.com/paper/2208.07239/) (2022)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey](https://mlsanity.com/paper/2005.07496/) (2020)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Line Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2010.10046/) (2020)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [How to transfer algorithmic reasoning knowledge to learn new algorithms?](https://mlsanity.com/paper/2110.14056/) (2021)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [Can neural networks learn persistent homology features?](https://mlsanity.com/paper/2011.14688/) (2020)
- [Line Graph Neural Networks for Link Weight Prediction](https://mlsanity.com/paper/2309.15728/) (2023)

## Built on by (most cited first, 2 of 2)

- [TMetaNet: Topological Meta-Learning Framework for Dynamic Link Prediction](https://mlsanity.com/paper/2506.00453/) (2025)
- [DyGSSM: Multi-view Dynamic Graph Embeddings with State Space Model Gradient Update](https://mlsanity.com/paper/2505.09017/) (2025)

## Abstract (arXiv)

Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.