CDL descriptors | Balaban distance connectivity indices

Balaban distance connectivity indices

Descriptor Category : topological
c++ entity: functor

Description

One of the most important topological indices, the Balaban distance connectivity index J (also called the distance connectivity index, or average distance sum connectivity) is also one of the most discriminating molecular descriptors and its value do not increase substantially with molecular size or number of rings; it is defined in terms of sums over each i row of the distance matrix D, i.e. the vertex distance degree sigma [Balaban 1982; Balaban 1983]. It is defined as:

**Equation 1:**Balaban distance connectivity index.

where B is the number of bonds, C the number of rings, and alpha is the vertex distance degree of the connected atoms.
To improve the discriminant capacity of the Balaban index, a new set of local vertex invariants (LOVI) was defined as ti = alphai / deltai, being deltai the vertex degree. When this LOVIs are used, the Balaban index is called Jt.

Prototype

  template <class Molecule>
  struct balaban_dist_connect_index : std::unary_function<Molecule,typename Molecule::calc_type> {

    result_type   operator()(const Molecule& m);

  };

Where defined

morpho/cdl/descriptors/topological.hpp

Namespace

morpho::cdl

Inherits from

std::unary_function<Molecule,typename Molecule::calc_type>

Arguments

Argument	Model of
`Molecule`	`cdl::molecule`

Example

same ol'story