Molecular invariants

The first proposed graphical bond order was calculated using the -> total path count P as a molecular invariant and is therefore denoted by the ratio (P / P)y, where i and j refer to the vertices incident to the bth bond erased from the graph [Randic, 1991b]. 

The row sums of this matrix contain information on the molecular folding in fact, in highly folded structures, they tend to be relatively small as the interatomic distances are small while the topological distances increase as the size of the structure increases. Therefore, the average row sum is a molecular invariant called the average distance/ distance degree, i.e. 

The average row sum of the distance matrix is a molecular invariant called the average distance degree defined as ... 

The minimum value of the vertex distance degrees is another molecular invariant called the unipolarity ... 

Other molecular invariants immediately derived from the distance matrix are the centralization Ao, variation Ao, and dispersion o, defined respectively as ... 

Using several increasing k values, a sequence of molecular invariants called the molecular profile is obtained as ... 

In this case, the row siuns of the geometry matrix are obtained by summing only the geometric distance powers of the atoms belonging to the periphery, and the average is found from the number of the contributing atoms only. Each atomic distance sum is considered as a local indicator of molecular shape, and each molecular invariant S is considered a global shape descriptor. 

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