Each vertex in the modular product is a pair of chemical bonds of the same type, one from R and one from P , representing a one-to-one correspondence between them. Here, we define the type of a chemical bond by the element types of the atoms involved in the bond (e.g., chemical bonds C-C and C=C are considered the same type, but different from C-O, C-N, etc.). In our approach, we intentionally omit differences in bond multiplicity to avoid "overfitting" to the positions of double or triple bonds, which can shift during chemical transformations, such as in pericyclic reactions. Additionally, we ignore chemical bonds involving hydrogen atoms to reduce computational complexity. For in- 1 and b ′ 2 do not share any atom of the products, or vice versa. Condition (1) implies that the two bond-to-bond correspondences map the same bond in the reactants to different bonds in the products, or vice versa, meaning that the combination of these mappings does not define a one-to-one correspondence between bonds in the reactants and products. For example, in Figure , vertices v 1 and v 2 are disconnected because they map (2) implies that the combination of the two mappings results in an atom-to-atom cor-respondence where the shared atom splits or merges during the reaction, which contradicts the principle of atom indivisibility. For instance, in Figure , vertices v 3 and v 5 are disconnected due to the condition (2)-the two mappings C