β-skeleton Shape-based Metrics for Large and Complex Graph Drawings

The shape-based metrics evaluate a drawing D of a large and complex graph G, by computing the similarity between G and a proximity graph S computed from D. However, existing metrics using planar proximity graphs, such as the Gabriel proximity graph with at most 3n−8 edges, fail to accurately evaluate drawings of complex dense graphs with Θ(n
²
) edges.This paper presents new shape-based faithfulness metrics using the β-skeleton proximity graph, which represent the skeleton shape of a set of points in the plane with up to Θ(n
²
) edges. Specifically, we leverage the effectiveness of the β-skeleton as a shape-based metric, and provide guidelines on the parameter β for various graph classes. Extensive experiments demonstrate that our new β-skeleton shape-based metrics can more accurately measure the faithfulness of drawings of large dense graphs, with a significant improvement of over 67% on average, than the existing Gabriel graph shape-based metrics.