Minimum depth graph embeddings and quality of the drawings: An experimental analysis

The depth of a planar embedding of a graph is a measure of the topological nesting of the biconnected components of the graph in that embedding. Motivated by the intuition that lower depth values lead to better drawings, previous works proposed efficient algorithms for finding embeddings with minimum depth. We present an experimental study that shows the impact of embedding depth minimization on important aesthetic criteria and relates the effectiveness of this approach with measures of how much the graph resembles a tree or a biconnected graph. In our study, we use a well known test suite of graphs obtained from real-world applications and a randomly generated one with favorable biconnectivity properties. In the experiments we consider orthogonal drawings computed using the topology-shape-metrics approach.