Lombardi Drawings of Graphs

TL;DR

This paper introduces Lombardi graph drawings, where edges are circular arcs and vertices have perfect angular resolution, along with algorithms for constructing such drawings for various graph classes.

Contribution

It defines Lombardi drawings and provides algorithms for creating them for regular, bounded degeneracy, and specific planar graphs.

Findings

Algorithms successfully produce Lombardi drawings for targeted graph classes.

Lombardi drawings ensure equal edge spacing around vertices with circular arc edges.

The approach extends the aesthetic and structural understanding of graph visualizations.

Abstract

We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.