The *edge-connectivity matrix*, denoted by ^{e}**χ**, of a graph *G* is the vertex-conectivity matrix of the corresponding line graph *L*(*G*). As an example, we give ^{e}**χ** of *L*(*G _{1}*) from Figure 11. The edge-degrees of

**Figure 17**. The edge-degrees in *G*_{1}and the vertex-degrees in *L*(*G*_{1}).

^{e}χ(G_{1})= |
0 |
0.577 |
0 |
0 |
0 |
0 |
0 |
||

0.577 |
0 |
0.333 |
0 |
0 |
0.289 |
0 |
|||

0 |
0.333 |
0 |
0.408 |
0 |
0.289 |
0 |
|||

0 |
0 |
0.408 |
0 |
0.408 |
0 |
0 |
|||

0 |
0 |
0 |
0.408 |
0 |
0.289 |
0.408 |
|||

0 |
0.289 |
0.289 |
0 |
0.289 |
0 |
0.354 |
|||

0 |
0 |
0 |
0 |
0.408 |
0.354 |
0 |

Summation of the elements in the upper (or lower) matrix-triangle gives the edge-connectivity index of *G _{1}*.