List of edge adjacency indices calculated by DRAGON

 

These are molecular descriptors calculated from the edge adjacency matrix of a molecule. The edge adjacency matrix is derived from the H-depleted molecular graph and encodes the connectivity between graph edges. It is a square symmetric matrix of dimension BxB, where B is the number of bonds between non-hydrogen atom pairs. The entries of the matrix equal one if the considered bonds are adjacent and zero otherwise.

 

The edge connectivity indices of order 0 (EPS0) and 1 (EPS1) are derived from the edge adjacency matrix in the same way as the Kier-Hall connectivity indices are derived from the vertex adjacency matrix, by replacing the vertex degree by the edge degree, i.e. the number of edges adjacent to a given edge in the H-depleted molecular graph [E. Estrada, N. Guevara, I. Gutman, J.Chem.Inf.Comput.Sci. 1998, 38, 428-431].

 

The spectral moments of the edge adjacency matrix (ESpmku, ESpmkx, ESpmkd, ESpmkr) are calculated by summing the diagonal elements of the kth power of the edge adjacency matrix. The order k of the spectral moment is given by the power order of the matrix [E. Estrada, J.Chem.Inf.Comput.Sci. 1996, 36, 844-849]; DRAGON provides spectral moments up to order 15 and applies a logarithmic transformation log(1 + ESPm).

The kth order spectral moment can be expressed as the linear combination of the counts of different structural fragments (subgraphs) in the graph. For example, the zero-order spectral moment corresponds to the number of edges in the graph. Several relations between spectral moments and fragment counts were derived by Estrada [E. Estrada, J.Chem.Inf.Comput.Sci. 1998, 38, 23-27; S. Markovic, I. Gutman, J.Chem.Inf.Comput.Sci. 1999, 39, 289-293].

 

By replacing the zero elements in the edge adjacency matrix diagonal with specific bond properties, new weighted edge adjacency matrices can be obtained, each encoding specific chemical information. DRAGON calculates three weighted edge adjacency matrices by using as the bond properties the edge degree (symbol x), the dipole moment (symbol d) and parameters related to the resonance integral (symbol r). The edge degree of a given bond is automatically calculated by the software, being the number of adjacent bonds. Dipole moment values for different bond-types are reported in the table below.

 

Bond type	Dipole moment	Bond type	Dipole moment
C – F	1.5	C = O	2.40
C – Cl	1.56	C – S	2.95
C(Cl)  – Cl	1.20	C = S	2.80
C(Cl)(Cl) – Cl	0.83	N – O	0.3
C – Br	1.48	N – [O –]	3.20
C – I	1.29	N = O	2.0
C – N	0.40	S – [O –]	2.90
C = N	0.9	C(*)(*)– C(*)(*)(*)	0.68
C # N	3.6	C(*)(*) – C	1.15
C – O	0.86	CC(*)(*)(*) =	1.48

 

The resonance-weighted edge adjacency matrix is obtained by replacing the diagonal elements of the edge adjacency matrix with parameters kC-X. 

The values of the parameter kC-X, which is used in the Hückel matrix and related to the resonance integral of the bond between the heteroatom X and the carbon atom C, proposed by Estrada and used in DRAGON are reported in the table below.

 

C – X bond	kC–X	C – X bond	kC–X
C  – C	1.0	C – S	0.7
C – N	0.9	C – F	0.7
C – O	0.8	C – Cl	0.4
C = O	1.2	C – Br	0.3
C - B	0.7	C - I	0.1

 

Eigenvalues from the three weighted edge adjacency matrices are also provided by DRAGON (EEigkx, EEigkd, EEigkr). For each molecular matrix the first 15 eigenvalues are retained. These molecular descriptors have not yet been proposed in the literature and therefore their meaning and role in QSAR modelling need to be a little more studied.