text: This document provides the foundations behind the functionality provided by the @math G library (this https URL), focusing on the basic operations the library provides: subsumption, refinement of directed labeled graphs, and distance similarity assessment between directed labeled graphs. @math G development was initially supported by the National Science Foundation, by the EAGER grant IIS-1551338.
  @cite_30: This paper reviews the use of similarity searching in chemical databases. It begins by introducing the concept of similarity searching, differentiating it from the more common substructure searching, and then discusses the current generation of fragment-based measures that are used for searching chemical structure databases. The next sections focus upon two of the principal characteristics of a similarity measure: the coefficient that is used to quantify the degree of structural resemblance between pairs of molecules and the structural representations that are used to characterize molecules that are being compared in a similarity calculation. New types of similarity measure are then compared with current approaches, and examples are given of several applications that are related to similarity searching.
  @cite_43: 
  @cite_17: A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection.
summary: Similarity measures for specific application domains, such as molecular structures in domains of biology or chemistry have also been studied @cite_30 , and they are typically grouped into three classes @cite_43 : sequence similarities (e.g., for DNA fragments), fingerprint-based (transform each molecule into a sequence of binary features representing whether a particular molecule exhibits particular properties or contains certain substructures) and graph-based (based on maximum common sub-graphs). The latter is a computationally expensive process, and thus there are a number of strategies to simplify the computations (e.g., @cite_17 ).