The measurement of the degree of symmetry proved to be a useful tool in the
prediction of quantitative structural-physical correlations. These measure
ments have been based, in the most general form, on the folding/unfolding a
lgorithm, for which we provide here a new and simpler proof. We generalize
this proof to the case of objects composed of more than one (full) orbit. A
n important practical issue we consider is the division of the graph into s
ymmetry orbits and the mapping of the symmetry group elements onto the poin
ts of the graph. The logical constraints imposed by the edges of the graph
are reviewed and used for the successful resolution of the coupling between
different orbits.