Shape-Faithful Graph Drawings

TL;DR

This paper investigates algorithms for creating shape-faithful graph drawings that accurately reflect the graph's structure using shape-based metrics, introducing new algorithms with significant improvements.

Contribution

It presents the first study on shape-faithful drawings for general graphs, proposing new algorithms based on force-directed and stress-based methods.

Findings

ShFR and ShSM outperform FR and SM in shape-based metrics

Experiments show 12% and 35% improvements respectively

Extensive comparison experiments validate the effectiveness

Abstract

Shape-based metrics measure how faithfully a drawing D represents the structure of a graph G, using the proximity graph S of D. While some limited graph classes admit proximity drawings (i.e., optimally shape-faithful drawings, where S = G), algorithms for shape-faithful drawings of general graphs have not been investigated. In this paper, we present the first study for shape-faithful drawings of general graphs. First, we conduct extensive comparison experiments for popular graph layouts using the shape-based metrics, and examine the properties of highly shape-faithful drawings. Then, we present ShFR and ShSM, algorithms for shape-faithful drawings based on force-directed and stress-based algorithms, by introducing new proximity forces/stress. Experiments show that ShFR and ShSM obtain significant improvement over FR (Fruchterman-Reingold) and SM (Stress Majorization), on average 12% and 35% respectively, on shape-based metrics.