Molecular hypergraphs

The first way. Molecular structures are represented by the labeled hypergraphs whose vertex and edge labels are elements of the symbolic alphabets. 

The vertex and edges alphabets of hypergraph H2 representing cyclopropenyl complex look like A V H2)) = CH, M and A E H2)) = [El, E2,E3,E4. The vertex labels are presented by symbols of functional chemical groups. It is easy to see that the vertex alphabets are the different for these hypergraphs. 

This way of hypergraph representation of molecular structures disregards the structure of ligands in the complexes. Yet it gives unambiguos descriptions, because the incidence matrices of the hypergraphs differ  

This example demonstrates the possibility of hypergraph modeling for molecular structure representation with the different degrees of accuracy. 

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Before defining a molecular hypergraph, we give several notions of hypergraph theory which are necessarily for further discussion [8, 73]. 

This example vividly illustrates the relationship between the structure of chemical compounds and the labels used in molecular hypergraphs. In particular, the labels of hyperedges E2 and Ei adequately reflect the essence of the metal-ligand bonds, in which ligands donate their electrons to form these bonds. 

I. Gutman, E.V. Konstantinova, V.A. Skorobogatov, Molecular Hypergraphs and Clar Structural Formulas of Benzenoid Hydrocarbons, Acta Chimia Hungaria - Models in Chemistry, 5-6 (1999) 539-548. 

In 1994 the concept of a molecular hypergraph, as a mathematical tool suitable for modeling the structure of molecules with polycentric bonds was introduced [46]. Main goal of this Lecture Notes is to demonstrate advantages of an application of hypergraph theory in chemical researches. 

E. Konstantinova and V. Skorobogatov. Molecular hypergraphs The new Representation of nonclassical molecular structures with polycentric delocalized bonds./. Chem. Inf Comput. Sci., 35 472-478,1995. 

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