ABSTRACT
Graphs are used as an efficient abstraction and approximation for diverse chemical systems, such as chemical compounds, ensembles ofmolecules, molecular fragments, polymers, chemical reactions, reaction mechanisms, and isomerization pathways. Obviously, the complexity of chemical systems is significantly reduced whenever they are modeled as graphs. For example, when a chemical compound is represented as a molecular graph, the geometry information is neglected, and only the atom connectivity information is retained. In order to be valuable, the graph representation of a chemical system must retain all important features of the investigated system and has to offer qualitative or quantitative conclusions in agreement with those provided by more sophisticated methods. All chemical systems that are successfully modeled as graphs have a common characteristic, namely they are composed of elements that interact between them, and these interactions are instrumental in explaining a property of interest of that chemical system. The elements in a system are represented as graph vertices, and the interactions between these elements are represented as graph edges. In a chemical graph, vertices may represent various elements of a chemical system, such as atomic or molecular orbitals, electrons, atoms, groups of atoms, molecules, and isomers. The interaction between these elements, which are represented as graph edges, may be chemical bonds, nonbonded interactions, reaction steps, formal connections between groups of atoms, or formal transformations of functional groups. The chapter continues with an overview of elements of graph theory that are important in chemoinformatics and in depicting two-dimensional (2D) chemical structures. Section 1.3 presents the most important types of chemical and molecular graphs, and Section 1.4 reviews the representation of molecules containing heteroatoms and multiple bonds with weighted graphs and molecular matrices.
