Two-Dimensional 2D Descriptors

Two matrices are particularly important, both of them based on the topological distance between vertices within a graph the distance matrix D(G) and the detour matrix A(G). The first contains as values the smallest number of steps from vertex i to vertex j, and the second contains as values the longest paths. For example, Equation (6.5) shows the D and A matrices of the DIOP ligand. 

Based on the matrix expression of molecular graphs, we can calculate the length of paths connecting any pair of atoms, i.e., a series of consecutive edges that connect two 

In another example, Chavali et al. demonstrated that 2D connectivity indices can give good structure/property correlations in molybdenum-catalyzed epoxidation [53,54]. They used the Computer Aided Molecular Design (CAMD) environment, a powerful computational tool used in product design. The method uses optimization techniques coupled with molecular design and property estimation methods, generating those molecular structures that match a desired set of properties. 

---

The weight and normalization functions are available for one- and two-dimensional (2D) descriptors. However, multidimensional calculations are performed technically in one dimension that is, each descriptor contains multiple one-dimensional vectors, such as [Xq,Xi,..., x , yoJu- ] Consequently, distance-related functions like transforms are performed only in the distance dimension, whereas general functions like weighting and normalization are calculated for an entire descriptor for example, normalization takes place on the entire vector instead of on the individual vectors of the first dimension. 

---