Editing Distance matrix (section)

=== Graph-theoretical Distance matrix ===
Distance matrix in chemistry that are used for the 2-D realization of molecular graphs, which are used to illustrate the main foundational features of a molecule in a myriad of applications.

[[File:Chem_DistanceMtrix.png|thumb|335x335px|Labeled tree representation of C<sub>6</sub>H<sub>14</sub>'s carbon skeleton based on its distance matrix]]
# Creating a label tree that represents the [[Skeletal formula|carbon skeleton]] of a molecule based on its distance matrix. The distance matrix is imperative in this application because similar molecules can have a myriad of label tree variants of their [[Skeletal formula|carbon skeleton]]. The labeled tree structure of [[hexane]] (C<sub>6</sub>H<sub>14</sub>) carbon skeleton that is created based on the distance matrix in the example, has different carbon skeleton variants that affect both the distance matrix and the labeled tree  
# Creating a labeled graph with edge weights, used in [[chemical graph theory]], that represent molecules with hetero-atoms.
# Le Verrier-Fadeev-Frame (LVFF) method is a computer oriented used to speed up the process of detecting the graph center in polycyclic graphs. However, LVFF requires the input to be a diagonalized distance matrix which is easily resolved by implementing the Householder tridiagonal-QL algorithm that takes in a distance matrix and returns the diagonalized distance needed for the LVFF method.