Distance matrix

The distance matrix indicates the distances, i.e., 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 distinguish between single and multiple bonds.

Example

(3- ethyl hexane )

In compact mathematical representation (without the atomic numbers), the properties are more clearly:

The distance matrix is symmetric. Since the graph is non-directional, the distance of atom 1 to atom intervals of the 2 to 2 atom atom is equal to 1

Use

The distance matrix is ​​used in the calculation of topological descriptors, such as the Wiener- index and, in modified form, the -J Balaban index.

To calculate the minimum plus matrix multiplication algorithm, the algorithm and Floyd Warshall or Dijkstra's algorithm can be applied to each node is used.