# Persistent Homology and Graphs Representation Learning

arXiv: https://arxiv.org/abs/2102.12926 · HTML: https://mlsanity.com/paper/2102.12926/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [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)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Graph Representation Learning: A Survey](https://mlsanity.com/paper/1909.00958/) (2019)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification](https://mlsanity.com/paper/1611.06345/) (2016)
- [Functional Summaries of Persistence Diagrams](https://mlsanity.com/paper/1804.01618/) (2018)
- [Fast Sequence-Based Embedding with Diffusion Graphs](https://mlsanity.com/paper/2001.07463/) (2020)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [Statistical Analysis of Persistence Intensity Functions](https://mlsanity.com/paper/1510.02502/) (2015)
- [Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology](https://mlsanity.com/paper/1707.06683/) (2017)
- [Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes](https://mlsanity.com/paper/1704.04561/) (2017)
- [Graph Based Analysis for Gene Segment Organization In a Scrambled Genome](https://mlsanity.com/paper/1801.05922/) (2018)

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

- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [On the Surprising Behaviour of node2vec](https://mlsanity.com/paper/2206.08252/) (2022)
- [Reliable Malware Analysis and Detection using Topology Data Analysis](https://mlsanity.com/paper/2211.01535/) (2022)
- [Alleviating neighbor bias: augmenting graph self-supervise learning with structural equivalent positive samples](https://mlsanity.com/paper/2212.04365/) (2022)
- [Positional Encoding meets Persistent Homology on Graphs](https://mlsanity.com/paper/2506.05814/) (2025)

## Abstract (arXiv)

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.