Limitations on Realistic Hyperbolic Graph Drawing

TL;DR

This paper demonstrates that certain hyperbolic graph drawing methods are limited by sub-constant feature separation, making hyperbolic geometry no more advantageous than Euclidean methods for these cases.

Contribution

It reveals fundamental limitations of hyperbolic graph drawing, showing that some require features to be so close they are indistinguishable from Euclidean distances.

Findings

Hyperbolic drawings require features separated by sub-constant distances.

Such features can be approximated by Euclidean distances.

Hyperbolic geometry offers no benefit over Euclidean drawing in these cases.

Abstract

We show that several types of graph drawing in the hyperbolic plane require features of the drawing to be separated from each other by sub-constant distances, distances so small that they can be accurately approximated by Euclidean distance. Therefore, for these types of drawing, hyperbolic geometry provides no benefit over Euclidean graph drawing.