Molecular Graphs and Molecular Hypergraphs of Organic Compounds: Comparative Analysis

Computer chemistry is a field of science appearing at the intersection of chemistry, mathematics and informatics. For the solution of any task in this field some mathematical representation of chemical structures is need. The most widely used approach to description of molecular structure is based on its representation as a graph G with vertices and edges corresponding to atoms and bonds of molecule. However, there may be other ways of describing the molecular structure. In this paper a number of methods to present the molecular structures of organic compounds (hydrocarbons) as hypergraphs Hk (k=1,2,…) of special type is suggested. Some results of comparison of graph and hypergraph molecular models are also given. Construction of Hk is defined by neighborhoods of k-th order for all vertices in a graph G corresponding to the carbon skeleton of molecule (k=1,2,…). Besides, analytical formulae, expressing the adjacency matrices of Hk throw adjacency matrix of corresponding graph G are obtained (k=1,2,…). The comparison of traditional graph model G and suggested hypergraph models Hk (k=1,2,…) is made by definite quantitative parameters, characterizing the efficiency of their applications in some tasks of computer chemistry. Some 4 different sets of structural formulae of hydrocarbons and 30 different quantitative parameters are used for these investigations. It is shown, that in 97% of all considered 120 cases the model H1 is superior to the model G, and in other cases these models are equivalent. However, the models Hk for k ≥ 2 are worse than G and H1. It is also shown on concrete examples, that in some cases, H1-models may be useful in constructing the structure-property correlations, since their use allows us to obtain more precise correlations than for G-models (in 75% of considered cases).