The existing paradigm for addressing constitutional isomerism relies upon the imposition of canonical forms to molecular structure where localised bond multiplicities are assigned to each atom-atom connection, and element valence is satisfied (a "valence structure"). While this approach has proved powerful and underpins digital representations of molecular structure, the imposition of canonical form hinders a more general description that captures the making and breaking of bonds. In our approach to constitutional isomerism, we focus only on atom-connectivity regardless of bond order. This complies with the IUPAC definition for connectivity. To illustrate shortcomings of the established approach compared with an atom-connectivity one, a [1,5]-sigmatropic rearrangement is examined (Fig. ). The rearrangement where both the reactant and product are drawn using standard canonical formseach featuring formal single and double bonds (Fig. ). The transition-state structure (TS) that links the reactant and product is drawn in such a way to indicate bonds being made and broken, including changes in bond multiplicity throughout the molecule. This TS is not, and indeed cannot, be represented in canonical form and thus would not be recognised using such approaches to constitutional isomerism. In Fig. , these same three structures are each drawn where only atom connectivity is shown (red); all structuresincluding the TSnow feature distinct atom-atom connectivity patterns. Note: explicit H-atoms are necessary here to avoid confusion with the more familiar canonical form representation where H-atoms are implicit. There exists a subtle limitation in using atom connectivity rather than canonical forms. For some reaction types (e.g., cycloadditions and chelotropic reactions) the formalism, in its basic form, "under-samples" the configuration space. This is explored later.