[vA]ij= 
The vertex-adjacency matrix of vertex-labeled multiple graph G is a square V × V matrix defined as:
[vA]ij= |
mij if vertices i and j are adjacent |
| 0 otherwise (6) |
where mij is the multiplicity of the i-j edge. In Figure 8, it is depicted a multiple graph G2. The corresponding vertex-adjacent matrix is also given.
Figure 8. Hydrogen-depleted and vertex-labeled multiple graph G2 representing one Kekulé structure of styrene.
vA(G2)= |
 |
0 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
 |
2 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|||
0 |
1 |
0 |
2 |
0 |
0 |
0 |
1 |
|||
0 |
0 |
2 |
0 |
1 |
0 |
0 |
0 |
|||
0 |
0 |
0 |
1 |
0 |
2 |
0 |
0 |
|||
0 |
0 |
0 |
0 |
2 |
0 |
1 |
0 |
|||
0 |
0 |
0 |
0 |
0 |
1 |
0 |
2 |
|||
0 |
0 |
1 |
0 |
0 |
0 |
2 |
0 |
G2