# Time-varying Extremum Graphs

arXiv: https://arxiv.org/abs/2406.17652 · HTML: https://mlsanity.com/paper/2406.17652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization](https://mlsanity.com/paper/2106.00157/) (2021)
- [Lifted Wasserstein Matcher for Fast and Robust Topology Tracking](https://mlsanity.com/paper/1808.05870/) (2018)
- [Scalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications](https://mlsanity.com/paper/1907.08325/) (2019)
- [Comparative Analysis of Merge Trees using Local Tree Edit Distance](https://mlsanity.com/paper/2111.04382/) (2021)
- [Jacobi Set Simplification for Tracking Topological Features in Time-Varying Scalar Fields](https://mlsanity.com/paper/2407.03348/) (2024)
- [TACHYON: Efficient Shared Memory Parallel Computation of Extremum Graphs](https://mlsanity.com/paper/2303.02724/) (2023)

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

- [BondMatcher: H-Bond Stability Analysis in Molecular Systems](https://mlsanity.com/paper/2504.03205/) (2025)
- [DebrisTracer: Reliable Tracking in Hypervelocity Impact Fast Imaging](https://mlsanity.com/paper/2607.15986/) (2026)

## Abstract (arXiv)

We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the TVEG as a time-varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the TVEG as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of TVEG towards identification and exploration of topological events such as deletion, generation, split, and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von K'arm'an vortex street dataset.