MOLECULAR SIMILARITY - I - ANALYTICAL, DESCRIPTION OF THE SET OF GRAPH SIMILARITY MEASURES

The elaboration of methods for defining molecular similarity measures is one of the important fields of modern theoretical chemistry. These measures are used for solving a number of problems of theoretical and computer chemistry, in particular the prediction of properties of chem ical compounds. For the construction of any molecular similarity measu res molecules are represented as some mathematical objects {M}, on whi ch quantitative similarity measures d(M-1, M-2) (M-1, M-2 is an elemen t of {M}) are introduced. The most widely used way of molecular repres entation is based on picturing molecules as labeled graphs, labels of which encode types of atoms and bonds. There are many-different simila rity measures defined for graphs, expressed in terms of vectors of gra ph invariant, sequences, and sets derived from graphs or in terms of m aximal common subgraph, etc. In general, there exists an infinite numb er of graph similarity measures. In the present paper an analytical de scription of-the set of symmetric similarity measures defined for arbi trary labeled graphs is given. The found general formula for the measu re depends on a number of parameters satisfying some conditions. Any p articular graph similarity measure maybe obtained from this formula at definite values of parameters.