Interweaving Mathematics and Art: Drawing Graphs as Celtic Knots and Links With CelticGraph

Area of Science:

• Graph theory
• Computational geometry
• Art history

Background:

• Celtic knots are an ancient art form symbolizing eternity and interconnectedness.
• Historically used in decorating monuments and manuscripts.
• Graph theory and network visualization are key areas of study.

Purpose of the Study:

• Introduce CelticGraph, a novel framework for illustrating graphs in the style of Celtic knots and links.
• Explore combinatorial concepts arising from generating these knot-like graph drawings.
• Develop a method for representing graph edges as smooth Bézier curves with limited curvature.

Main Methods:

• Developed the CelticGraph framework for graph visualization.
• Employed a novel algorithm to represent graph edges as Bézier curves.
• Investigated the computation of 4-regular plane graphs using the framework.

Main Results:

• Demonstrated that CelticGraph can represent any 4-regular plane graph as a Celtic knot or link.
• Achieved smooth curve representations for graph edges with limited curvature.
• Implemented CelticGraph as an add-on for the Vanted network visualization tool.

Conclusions:

• The CelticGraph framework successfully visualizes graphs as Celtic knots and links.
• The underlying methods connect graph theory with artistic representations.
• This approach offers a new perspective on network visualization and analysis.