A minimal set of cut point atoms are specified as follows: In this example, 2, 7, 8, and 9 are specified and identify the moiety highlighted in green. Number 8 being the C of the nucleophile attack, 9 the Cl, 7 the entrance to the ring and 2 being any other member of this ring. The meaning is as follows: we determine the paths between all cut-point atoms, the members of the moiety are along these paths between the cut points. However, at every cut-point only those paths that link to another cut-point will be included. With cyclic structures we also need to constrain that not any path will be accepted, but only the shortest path; and finally, that paths are included in the order of the cut-points specified, in such a way that the next path added is the one which has the least number of "forbidden bonds". A "forbidden bond" is one which is cut out and not included by the previous cut-point atoms. For example, in this intermediate structure the bond from C to O is a forbidden bond because it was not already included by any path to another cut-point atom. This is the most parsimonious way to delineate moieties in any molecular structures by the smallest number of atoms, and this system can be canonicalized, for example, atom 4 or 3 could have been specified instead of 2 to "cut out" the same moiety, but 2 is the lowest InChI atom number so 2 is chosen. This approach establishes a parsimonious minimal atom mapping, and all other atom mappings can be computed from there. This is similar to the fact that when we have mapped the atoms of the reaction center, then the other atoms mappings farther away from the center all follow.