Shape-Faithful Graph Drawings

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.