Distance matrix
The distance matrix shows the distances, i.e. that is, the number of bonds between the atoms of a molecule . The distance matrix thus describes an important aspect of the topology of a chemical compound. The molecule is viewed as an undirected graph without multiple edges . The bond orders are thus ignored, a distance matrix does not differentiate between single and multiple bonds.
example
.PNG)
(3-ethylhexane)
| atom | 1 | 2 | 3 | 4th | 5 | 6th | 7th | 8th |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 2 | 3 | 4th | 5 | 3 | 4th |
| 2 | 1 | 0 | 1 | 2 | 3 | 4th | 2 | 3 |
| 3 | 2 | 1 | 0 | 1 | 2 | 3 | 1 | 2 |
| 4th | 3 | 2 | 1 | 0 | 1 | 2 | 2 | 3 |
| 5 | 4th | 3 | 2 | 1 | 0 | 1 | 3 | 4th |
| 6th | 5 | 4th | 3 | 2 | 1 | 0 | 4th | 5 |
| 7th | 3 | 2 | 1 | 2 | 3 | 4th | 0 | 1 |
| 8th | 4th | 3 | 2 | 3 | 4th | 5 | 1 | 0 |
In a compact mathematical representation (without the atomic numbers) the properties become clearer:
The distance matrix is symmetrical. Since the graph is undirected, the distance from atom 1 to atom 2 is equal to the distance from atom 2 to atom 1.
use
The distance matrix is used to calculate topological descriptors such as the Wiener index and, in a modified form, the Balaban J index .
The Min-Plus matrix multiplication algorithm , the Floyd and Warshall algorithm , or the Dijkstra algorithm applied to each node can be used for the calculation.