Determining the map between two arbitrary graphs is the well-known subgraph matching problem , and as an NP-complete problem it is generally costly to compute. However, in this work the graphs typically represent valence chemical environments and this fact can be used to simplify the problem. The typical size of the graphs considered in this work when finding parameters is generally small, requiring a minimum of 1, 2, 3, or 4 nodes for chemical environments of atoms, bonds, angles, or torsions, respectively. This set is the primary nodes in the graph, and all other nodes in the graph can be categorized by their depth in the graph, or the shortest path to any of the primary nodes. The primary nodes have a depth of 0, and any additional nodes have a depth larger than 0. We refer to this number in subsequent sections as the graph depth d.