The expression 2 𝑁(𝑁-1) 2 ⁄ places an upper bound on any enumeration; any imposed constraints will reduce the total number. Valence and steric considerations place obvious limitations on the maximum number of atom connections any atom in the set may form, greatly reducing the number of realistic atom-connectivity configuration combinations. Indeed, previous methods of isomer enumeration relied heavily upon the restrictions imposed by valence. Another constraint concerns minimal connectivity where existing isomer-enumeration approaches impose the requirement that the atom-connectivity configurations (the species) must constitute a single connected entity thus complying with the IUPAC definitions for constitution and constitutional isomerism.