# Deep Graph Mapper: Seeing Graphs through the Neural Lens

arXiv: https://arxiv.org/abs/2002.03864 · HTML: https://mlsanity.com/paper/2002.03864/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 22 of 22)

- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [A Survey on Graph-Based Deep Learning for Computational Histopathology](https://mlsanity.com/paper/2107.00272/) (2021)
- [GCExplainer: Human-in-the-Loop Concept-based Explanations for Graph Neural Networks](https://mlsanity.com/paper/2107.11889/) (2021)
- [Simplicial Complex Representation Learning](https://mlsanity.com/paper/2103.04046/) (2021)
- [Spatio-Spectral Graph Neural Networks](https://mlsanity.com/paper/2405.19121/) (2024)
- [Taxonomy of Benchmarks in Graph Representation Learning](https://mlsanity.com/paper/2206.07729/) (2022)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Topological Pooling on Graphs](https://mlsanity.com/paper/2303.14543/) (2023)
- [Graph Convolutional Networks for Multi-modality Medical Imaging: Methods, Architectures, and Clinical Applications](https://mlsanity.com/paper/2202.08916/) (2022)
- [Saliency-Aware Regularized Graph Neural Network](https://mlsanity.com/paper/2401.00755/) (2024)
- [Topological structure of complex predictions](https://mlsanity.com/paper/2207.14358/) (2022)
- [TopER: Topological Embeddings in Graph Representation Learning](https://mlsanity.com/paper/2410.01778/) (2024)
- [Rhomboid Tiling for Geometric Graph Deep Learning](https://mlsanity.com/paper/2505.09586/) (2025)
- [TopoFormer: Topology Meets Attention for Graph Learning](https://mlsanity.com/paper/2607.28259/) (2026)
- [NervePool: A Simplicial Pooling Layer](https://mlsanity.com/paper/2305.06315/) (2023)
- [Simplicity within biological complexity](https://mlsanity.com/paper/2405.09595/) (2024)
- [A Mapper Algorithm with implicit intervals and its optimization](https://mlsanity.com/paper/2412.11631/) (2024)
- [Structured Learning on Mapper Representations](https://mlsanity.com/paper/2608.22044/) (2026)

## Abstract (arXiv)

Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they are not equally suitable for visualisation purposes. In this work, we merge Mapper, an algorithm from the field of Topological Data Analysis (TDA), with the expressive power of Graph Neural Networks (GNNs) to produce hierarchical, topologically-grounded visualisations of graphs. These visualisations do not only help discern the structure of complex graphs but also provide a means of understanding the models applied to them for solving various tasks. We further demonstrate the suitability of Mapper as a topological framework for graph pooling by mathematically proving an equivalence with Min-Cut and Diff Pool. Building upon this framework, we introduce a novel pooling algorithm based on PageRank, which obtains competitive results with state of the art methods on graph classification benchmarks.