# Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

arXiv: https://arxiv.org/abs/1707.06683 · HTML: https://mlsanity.com/paper/1707.06683/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2017.

## Built on by (most cited first, 8 of 8)

- [Simplicial Complex Representation Learning](https://mlsanity.com/paper/2103.04046/) (2021)
- [Persistent Homology and Graphs Representation Learning](https://mlsanity.com/paper/2102.12926/) (2021)
- [Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis](https://mlsanity.com/paper/2401.03194/) (2024)
- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [DGSVis: Visual Analysis of Hierarchical Snapshots in Dynamic Graph](https://mlsanity.com/paper/2205.13220/) (2022)
- [Neural Persistence Dynamics](https://mlsanity.com/paper/2405.15732/) (2024)
- [Detecting Narrative Shifts through Persistent Structures: A Topological Analysis of Media Discourse](https://mlsanity.com/paper/2506.14836/) (2025)
- [Synergistic Fusion of Topological Structure and Temporal Semantics of Mobility for Urban Region Embedding](https://mlsanity.com/paper/2609.08268/) (2026)

## Abstract (arXiv)

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics.