# PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction

arXiv: https://arxiv.org/abs/2404.15225 · HTML: https://mlsanity.com/paper/2404.15225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 81 references that are in the map.
- First posted on arXiv 23 Apr 2024.

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

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [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 Neural Networks for Link Prediction with Subgraph Sketching](https://mlsanity.com/paper/2209.15486/) (2022)
- [Neo-GNNs: Neighborhood Overlap-aware Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2206.04216/) (2022)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Neural Link Prediction with Walk Pooling](https://mlsanity.com/paper/2110.04375/) (2021)
- [Graph InfoClust: Leveraging cluster-level node information for unsupervised graph representation learning](https://mlsanity.com/paper/2009.06946/) (2020)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [Pure Message Passing Can Estimate Common Neighbor for Link Prediction](https://mlsanity.com/paper/2309.00976/) (2023)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [A Topological Perspective on Demystifying GNN-Based Link Prediction Performance](https://mlsanity.com/paper/2310.04612/) (2023)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Explaining the Power of Topological Data Analysis in Graph Machine Learning](https://mlsanity.com/paper/2401.04250/) (2024)

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

- [Transfer Learning for Temporal Link Prediction](https://mlsanity.com/paper/2504.10925/) (2025)
- [Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning](https://mlsanity.com/paper/2604.26370/) (2026)

## Abstract (arXiv)

Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models have achieved high performance in LP, understanding why they perform well is challenging because most comprise complex neural networks. We employ persistent homology (PH), a topological data analysis method that helps analyze the topological information of graphs, to interpret the features used for prediction. We propose a novel method that employs PH for LP (PHLP) focusing on how the presence or absence of target links influences the overall topology. The PHLP utilizes the angle hop subgraph and new node labeling called degree double radius node labeling (Degree DRNL), distinguishing the information of graphs better than DRNL. Using only a classifier, PHLP performs similarly to state-of-the-art (SOTA) models on most benchmark datasets. Incorporating the outputs calculated using PHLP into the existing GNN-based SOTA models improves performance across all benchmark datasets. To the best of our knowledge, PHLP is the first method of applying PH to LP without GNNs. The proposed approach, employing PH while not relying on neural networks, enables the identification of crucial factors for improving performance.