To precisely describe the [exact] subgraph isomorphism problem [ ], let G p = (V p , E p ) and G q = (V q , E q ) be the graph representations of the parent crystal structure and query fragment, respectively, with V • and E • the set of nodes and edges, respectively. Let s : V p ∪ V q → {H, He, Li, Be, ..., No, Lr} be the node-labeling function that maps a node to the chemical species it represents. A subgraph G p = (V p , E p ) of the parent graph G p (subgraph =⇒ V p ⊆ V p and E p ⊆ E p ) is isomorphic to the query graph G q if there exists a bijection θ : V p → V q such that {v p,i , v p,j } ∈ E p ⇐⇒ {θ(v p,i ), θ(v p,j )} ∈ E q and s(v p ) = s(θ(v p )) for all v p ∈ V p . The subgraph isomorphism problem is to find all subgraphs G p of G p isomorphic to G q .