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

Abstract

Celtic knots, an ancient art form often linked to Celtic heritage, have been used historically in the decoration of monuments and manuscripts, often symbolizing the notions of eternity and interconnectedness. This paper introduces the framework CelticGraph designed for illustrating graphs in the style of Celtic knots and links. The process of creating these drawings raises interesting combinatorial concepts in the theory of circuits in planar graphs. Further, CelticGraph uses a novel algorithm to represent edges as Bézier curves, aiming to show each link as a smooth curve with limited curvature. We also show that with our production mechanisms we can compute any 4-regular plane graph and thereby any celtic knot or link. The CelticGraph framework for drawing graphs as celtic knots and links is implemented as an add-on of Vanted, a network visualization and analysis tool.