Information theory graph complexity

On the basis of graph theory and information theory, Bertz [30] has proposed, in the past few years, the first general index of molecular complexity (T ), so introducing a quantitative concept of "molecular complexity" which may be applied to synthetic analysis. 

The Bertz index incorporates skeletal complexity by representing the molecular structure as a graph (a skeletal molecular graph that represents all nonhydrogen atoms) that will have properties that are expressed as so-called graph theoretical invariants. Bertz uses information theory to incorporate the effects of symmetry, and also accounts for molecular size and the presence of heteroatoms in his general index of complexity. 

In the "general index of complexity" (C ) proposed by Bertz, besides the number of connections, symmetry is also taken into account. Such an index, that incorporates concepts from the "graph theory" and the "theory of information" [7] is defined as ... 

In Chapter 1 we have stated that the classical structural theory is the only way to "visualise" the synthesis of a more or less complex organic compound. However, all or most of the information given by a structural formula can also be expressed.by a matrix (see also Appendix A-1). There are different kinds of matrices for example, the adjacency matrix J, which originates in graph theory and indicates only which atoms are bonded, or the connectivity matrix C, whose off-diagonal entries are the formal covalent bond orders. For instance, the corresponding matrices of hydrogen cyanide are ... 

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

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