How to Draw a Planar Graph: An Experimental Evaluation

2026-07-25

AI Summary

Existing planar graph drawing algorithms lack systematic evaluation with respect to visual aesthetics, making it difficult to identify a universally optimal approach. This study presents the first large-scale experimental comparison of classical algorithms, force-directed layouts, stress-based models, and novel methods specifically optimized for edge-length uniformity, area balance, and angular resolution across small to medium-sized graphs. The findings reveal that no single algorithm dominates across all aesthetic criteria; however, targeted optimizations effectively enhance specific visual properties. Moreover, a scoring-guided strategy that combines multiple layout methods substantially improves overall drawing quality. These results provide empirical guidance for algorithm selection and design, yet the development of a general-purpose, robust planar graph drawing method remains an open challenge.

Abstract

Planar graphs are central to graph drawing, with extensive results on planar layouts and related structures. Every planar graph admits a planar straight-line drawing, and algorithms can guarantee additional geometric or combinatorial properties. However, it is unclear which algorithms work best in practice. Even for small graphs with near-perfect manual drawings, standard algorithms might produce poor spacing, distorted faces, or small angles. We present an experimental evaluation of planar graph drawing algorithms on a large benchmark collection of small and medium-sized planar graphs (\(10\)--\(400\) vertices). The study compares established algorithms from the graph drawing literature, practical force-directed and pressure-based heuristics, and new optimization-based methods that directly improve visual properties such as edge-length uniformity, face-area balance, and angular resolution. The results show that no evaluated algorithm is best across all aesthetic criteria, and optimizing one visual property often worsens another. Directly optimizing visual criteria improves targeted scores, and score-guided combination of several methods gives the best aggregate results, but no simple algorithm emerges as a clear universal default. Designing a simple, robust algorithm that performs well across graph families and aesthetic criteria therefore remains an open practical problem.

Problem

• planar graph drawing
• aesthetic criteria
• algorithm evaluation
• visual properties
• graph layout

Innovation

• planar graph drawing
• experimental evaluation
• visual optimization
• aesthetic criteria
• algorithm comparison