Until 1969 there was no obvious relationship except that the two methods lead to the same predictions. As noted earlier, the Woodward–Hoffmann method requires symmetry. But in 1969 and 1970 a general formulation was published, namely, A ground-state pericyclic change is symmetry-allowed when the total number of (4q + 2) and (4r) components is odd. The 1969–1970 Woodward–Hoffmann general formulation is seen to be  equivalent to the Zimmerman Möbius–Hückel concept. Thus each (4r) component provides one plus-minus overlap in the cyclic array (i.e. an odd number) for 4n electrons. The (4q + 2) component just makes certain that the number of electrons in symmetric bonds is 4n + 2.
The equivalency of the more recent formulation of the Woodward–Hoffmann rules has been discussed.