Graph Drawing by Weighted Constraint Relaxation

A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using a relaxation method that considers a single pair of vertices at a time. Our results show that relaxation can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then present various real-world applications to show how the unique properties of relaxation make it easier to produce constrained layouts than previous approaches. We also show how relaxation can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs.