# Dioscuri Centre in

Topological Data
Analysis

## Real world problems. Rigorous mathematics. Efficient solutions.

# Knot invariants and their relations: a topological perspective

This page contains accompagning and additional interactive plots for P. Dłotko, D. Gurnari, and R. Sazdanovic,

*Mapper-type algorithms for complex data and relations*(2024) DOI 10.1080/10618600.2024.2343321. All data and code can be found at DOI 10.5281/zenodo.10876347.

Below some additional interactive examples can be found. All graphs can be zoomed in and saved to png using the icons in the toolbar.

**BallMapper graphs**

Interactive graphs of the space of different knots polynomials. Different coloring functions can be choosen using the drop-down menu.

**Maps between BallMapper graphs**

Examples of how knots in some clusters in a BallMapper graph are mapped into another BallMapper graph of different polynomials coefficients of the same sets of knots. Cluster in the left-hand side graph can be selected either by clicking or using the drop-down list. The COLOR button colors the right-hand graph by assigning to each of the nodes the percentage of its covered knots that are covered by the subset of nodes selected in the left-hand graph.

**KnotInfo BallMapper graphs**

Interactive graphs of the space of different knots polynomials, constructed from the data publicly available at KnotInfo. Different coloring functions can be choosen using the drop-down menu. Code to recreate (and inspect) these graphs can be found on this repository.