List of connectivity descriptors calculated by DRAGON

 

Connectivity indices are among the most popular topological indices. They are calculated from a the H-depleted molecular graph where each vertex (non-hydrogen atom) is weighted by the vertex degree, i.e. the number of connected non-hydrogen atoms [L.B. Kier, L.H. Hall, Molecular Connectivity in Structure-Activity Analysis, Research Studies Press - Wiley, Chichester (UK), 1986]. 

The general formula for connectivity indices is:

 

where k runs over all of the mth order subgraphs constituted by n atoms (n = m + 1 for acyclic subgraphs); K is the total number of mth order subgraphs present in the molecular graph. The product is over the vertex degrees d of all the vertices involved in each subgraph. The subscript "q" refers to the type of molecular subgraph and is ch for chain or ring, pc for path-cluster, c for cluster, and p for path (that can also be omitted). DRAGON calculates only connectivity indices for path subgraphs (p) of order 0 up to 5.

 

The connectivity indices Xk, k being the order, are derived from the simple vertex degrees d. The connectivity index X1 is usually known as the Randic connectivity index. Average connectivity indices XkA are obtained by dividing each connectivity index by the number of paths involved in its calculation.

By replacing the vertex degree d by the valence vertex degree dn in the formula reported above, similar valence connectivity indices Xkv have been defined [L.B. Kier, L.H. Hall, J.Pharm.Sci. 1981, 70, 583-589], able to account for the presence of heteroatoms in the molecule as well as double and triple bonds.

 

Average valence connectivity indices XkAv are obtained by dividing each valence connectivity index by the number of paths involved in its calculation.

 

Solvation connectivity indices Xksol are calculated by a modified formula where the inner product contemporarily accounts for vertex degrees and principal quantum numbers. These molecular descriptors are defined for a H-depleted molecular graph, where fluorine atoms as well as hydrogens are not taken into account, their dimension being very close to that of the hydrogen atom.

 

The modified Randic connectivityindex XMOD is a molecular descriptor proposed as the sum of atomic properties, accounting for valence electrons and extended connectivities in the H-depleted molecular graph using a Randic connectivity index-type formula [H. Lohninger, J.Chem.Inf.Comput.Sci. 1993, 33, 736-744].

 

The reciprocal distance Randic type-index RDCHI is defined on the analogy of the Randic connectivity index X1, where the vertex degrees are substituted by the row sums of the reciprocal distance matrix [O. Ivanciuc, T.-S. Balaban, A.T. Balaban, J.Math.Chem. 1993, 12, 309-318]. Moreover, the reciprocal distance squared Randic type-index RDSQ is obtained from the RDCHI index substituting the exponent –1/2 with 1/2.