The field of chemical graph theory utilizes simple graphs as models of molecules. These models are called molecular graphs, and quantifiers of molecular graphs are known as molecular descriptors or topological indices. Today's chemists use molecular descriptors to develop algorithms for computer aided drug designs, and computer based searching algorithms of chemical databases and the field is now more commonly known as combinatorial or computational chemistry. With the completion of the human genome project, related fields are emerging such as chemical genomics and pharmacogenomics. Recent advances in molecular biology are driving new methodologies and reshaping existing techniques, which in turn produce novel approaches to nucleic acid modeling and protein structure prediction. The origins of chemical graph theory are revisited and new directions in combinatorial chemistry with a special emphasis on biochemistry are explored. Of particular importance is the extension of the set of molecular descriptors to include graphical invariants. We also describe the use of artificial neural networks (ANNs) in predicting biological functional relationships based on molecular descriptor values. Specifically, a brief discussion of the fundamentals of ANNs together with an example of a graph theoretic model of RNA to illustrate the potential for ANN coupled with graphical invariants to predict function and structure of biomolecules is included.

The secondary structures of ribonucleic acid (RNA) have been successfully modeled with graph-theoretic structures. Often, simple graphs are used to represent secondary RNA structures; however, in this research, a multigraph representation of RNA is used, in which vertices represent stems and edges represent the internal motifs. Any type of RNA secondary structure may be represented by a graph in this manner. We define novel graphical invariants to quantify the multigraphs and obtain characteristic descriptors of the secondary structures. These descriptors are used to train an artificial neural network (ANN) to recognize the characteristics of secondary RNA structure. Using the ANN, we classify the multigraphs as either RNA-like or not RNA-like. This classification method produced results similar to other classification methods. Given the expanding library of secondary RNA motifs, this method may provide a tool to help identify new structures and to guide the rational design of RNA molecules.