Matrices Derived from the Adjacency Matrix

A is used to generate the distance matrix D [8-10]. D is a square n x n symmetric matrix in which the entry (D),y indicates the distance between vertices i and j, where the distance is the minimum number of edges between i and j. The maximum distance in D is denoted as dmax. D of G-I is 

Further, A is used to generate the valence vector, v [11]. This vector indicates the vertex degree for each atom in G  

The value of 3 for the third and fourth atoms in v, for example, indicates that both atoms have three neighbor atoms. A value of 1 indicates terminal atoms. 

Estrada [13] proposes the use of the edge-adjacency matrix, E, to develop new molecular descriptors. For example, G-I has five edges, which can be labeled in the following way  

By considering each edge as a vertex, and connecting a pair of these vertices if they present two incident edges in G-I, the following edge-adjacency graph E-I is obtained  

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