Spring algorithms and symmetry

Spring algorithms are effective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric structures of graphs. This feature has been confirmed by numerous experiments. In this paper, we firstly 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 spring algorithms can display graph symmetry. Finally, the strength of our general theorem is demonstrated from its application to several existing spring algorithms.

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