Spring algorithms and symmetry - Eades, Peter; Lin, Xuemin (Theoretical computer science, 2000)
Spring algorithms are regarded as effective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric properties of graphs. This feature has been confirmed by numerous experiments. In this paper, firstly we formalize the concepts of graph symmetries in terms of “reflectional” and “rotational” automorphisms; and characterize the types of symmetries, which can be displayed simultaneously by a graph layout, in terms of “geometric” automorphism groups. We show that our formalization is complete. Secondly, we provide general theoretical evidence of why many spring algorithms can display graph symmetry. Finally, the strength of our general theorem is demonstrated from its application to several existing spring algorithms.