# Frequent subgraph-based persistent homology for graph classification

arXiv: https://arxiv.org/abs/2512.24917 · HTML: https://mlsanity.com/paper/2512.24917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [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)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes](https://mlsanity.com/paper/2001.02581/) (2020)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [A Survey on Graph Classification and Link Prediction based on GNN](https://mlsanity.com/paper/2307.00865/) (2023)
- [Cluster-guided Contrastive Class-imbalanced Graph Classification](https://mlsanity.com/paper/2412.12984/) (2024)
- [cgSpan: Closed Graph-Based Substructure Pattern Mining](https://mlsanity.com/paper/2112.09573/) (2021)
- [Representation Learning for Frequent Subgraph Mining](https://mlsanity.com/paper/2402.14367/) (2024)
- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [Mining Frequent Patterns in Evolving Graphs](https://mlsanity.com/paper/1809.00394/) (2018)
- [FreSCo: Mining Frequent Patterns in Simplicial Complexes](https://mlsanity.com/paper/2201.08005/) (2022)

## Abstract (arXiv)

Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods on graphs rely on a limited set of filtrations, such as degree-based or weight-based filtrations, which overlook richer features like recurring information across the dataset and thus restrict expressive power. In this work, we propose a novel graph filtration called Frequent Subgraph Filtration (FSF), which is derived from frequent subgraphs and produces stable and information-rich frequency-based persistent homology (FPH) features. We study the theoretical properties of FSF and provide both proofs and experimental validation. Beyond persistent homology itself, we introduce two approaches for graph classification: an FPH-based machine learning model (FPH-ML) and a hybrid framework that integrates FPH with graph neural networks (FPH-GNNs) to enhance topology-aware graph representation learning. Our frameworks bridge frequent subgraph mining and topological data analysis, offering a new perspective on topology-aware feature extraction. Experimental results show that FPH-ML achieves competitive or superior accuracy compared with kernel-based and degree-based filtration methods. When integrated into graph neural networks, FPH yields relative performance gains ranging from 0.4 to 21 percent, with improvements of up to 8.2 percentage points over GCN and GIN backbones across benchmarks.