The potential energy landscape (PEL) is a function across the configurational space of nuclei (arising from the Born-Oppenheimer approximation), having dimension 3N, where N is the number of nuclei. The PEL is often defined in the context of additive contributions associated with many-body interactions -either from decomposition of first-principles calculations (i.e. energy decomposition analysis), or as a groundup approach for the construction of the total potential energy function as is done with classical physics implementations. Broadly, the topological features of PEL include the locations of the maxima and minima, the critical points of different indices, and potentially information about the gradients (dE/dr) along specific dimensions r. Although a breadth of mathematical tools exist to describe topological features in the broader context of functions in real space, their application to the study of PEL is somewhat limited. Historically, and for the sake of convenience, chemists often focus upon select portions of an energy landscape; for example, how a specific basin may be connected to another through the lowest energy pathway (via a critical point of index 1, a traditional transition state). In this instance, disconnectivity graphs are a widely employed visualization and analytical tool that have had numerous applications, as in mapping protein folding pathways. A disconnectivity graph is a reductive summary of an energy landscape as a tree. The vertices of the tree correspond to critical points of index 0 and 1, with local minima appearing as leaves, and with the lowest energy saddle point connecting two minima appearing as internal nodes. Each edge in the tree corresponds to a minimum energy path connecting two critical points.