balaban_j_index

skfp.descriptors.balaban_j_index(mol: Mol, distance_matrix: ndarray | None = None) → float

Balaban’s J Index.

Calculates the Balaban’s J index [1], defined as a measure of molecular connectivity with an emphasis on cyclic structures. The formula for calculating Balaban’s J Index is given as:

\[J = \frac{M}{μ + 1} \cdot \frac{Σ_{ij} (d_{ij})^{-1}}{n},\]

where:

• \(M\) is the number of bonds

• \(μ\) is the cyclomatic number (number of independent cycles)

• \(d_{ij}\) is the distance between atoms \(i\) and \(j\)

• \(n\) is the number of atoms

Parameters:

• mol (RDKit Mol object) – The molecule for which the Balaban’s J index is to be calculated.

• distance_matrix (np.ndarray, optional) – Precomputed distance matrix. If not provided, it will be calculated by RDKit.

References

[1]

Balaban, Alexandru T. “Highly discriminating distance-based topological index.” Chemical Physics Letters 89.5 (1982): 399-404.

Examples

>>> from rdkit.Chem import MolFromSmiles
>>> from skfp.descriptors import balaban_j_index
>>> mol = MolFromSmiles("C1=CC=CC=C1")  # Benzene
>>> balaban_j_index(mol)
3.000000000000001