Topological path

The topological-path RDF is derived from the bond-path RDF. This type simply uses the number of bonds (instead of r j) between the atom pairs along the shortest path. 

Depending on the task, topological path descriptors are represented in either peak mode (i.e similar to a distance pattern) or in the conventional smoothed mode containing the probability distribution. With analysis methods that rely on interpolation, like neural networks, the smoothed representation is necessary to preserve interpolation features. 

In addition, three distance modes — Cartesian, bond-path, and topological-path distances — are compared. Cartesian RDF descriptors are usually quite sensitive to small constitntional changes in the molecule. The bond-path descriptors exhibit less sensitivity, whereas topological bond-path descriptors only indicate extreme changes in the entire molecnle or in the size of the molecule. 

Topological Path describes the number of the bonds along the shortest bond path between two atoms. 

The number of aromatic bonds minimum, average, and maximum value of the aromaticity of the aromatic bonds percentage of aromatic bonds number of aromatic molecular zones or aromaticity of the peripheral topological path can be calculated as descriptors. Some descriptors simultaneously reflect the aromaticity and size of the molecule. Other descriptors reflect the concentration of aromaticity in small areas of the molecule. 

Non-aromaticity of peripheral topological path because of the discontinuous conjugation. 

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