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A disconnectivity graph summarizes how local minima of an energy landscape become connected as the allowed maximum energy increases. Each terminal branch represents a basin around a local minimum. Two branches merge at the lowest threshold for which a permitted path joins their basins without exceeding that threshold. Vertical height therefore carries barrier information; horizontal spacing is usually chosen for readability.

For example, two low-energy states may sit at similar energies but merge only high in the graph, indicating a difficult transition between them. A cluster of branches merging low down instead suggests easy rearrangement within that group. The graph is useful for separating energetic preference from kinetic accessibility in thermal activation. It does not determine transition rates by itself: the allowed dynamics, path widths and kinetic prefactors remain necessary. Changing the permitted moves changes which paths exist and can therefore change the graph.

A disconnectivity graph joins minima when an energy threshold first permits a path between their basins. Taking thresholds in steps of 2 and admitting transition states with energy at most the threshold gives the following merges:

These eight merges connect all nine minima without duplicating a basin. Minimum endpoints lie at their stated energies; branch heights are the discretized superbasin thresholds, not necessarily the exact saddle energies. If a strictly-less-than threshold convention is used, barriers exactly on a grid line join at the next grid level; the physical connectivity is unchanged.