An Heuristic for Graph Symmetry Detection

We give a short introduction to an heuristic to nd automorphisms in a graph such as axial, central or rotational symmetries. Using technics of factorial analysis, we embed the graph in an Euclidean space and try to detect and interpret the geometric symmetries of of the embedded graph. 1. Introduction Testing whether a graph has any axial (rotational, central, respectively) symmetry is a NP-complete problem 9]. Some restrictions (central symmetry with exactly one xed vertex and no xed edge) are polynomialy equivalent to the graph isomor-phism test. Notice that this latter problem is not known to be either polynomial or NP-complete in general. But several heuristics are known (e.g. 3]) and several restrictions leads to eecient algorithms: linear time isomorphism test for planar graphs 6] and interval graphs 8], polynomial time isomorphism test for xed genus 10, 5], k-contractible graphs 12] and pairwise k-separable graphs 11], linear axial symmetry detection for planar graphs with a given embedding. In the context of automatic generation of industrial diagrams, the aim of symmetry display is not only to get a 'nice' drawing but also to enlight some of the semantic of the design. Usually the given networks are not planar and even so, due to other constraints (even aesthetics ones), crossings are very common. We present here the main outlines of an heuristic to detect symmetries. It will soon be integrated in PICTEL, our diagram drawing module of CATIA R