The edge-connectivity matrix, denoted by eχ, of a graph G is the vertex-conectivity matrix of the corresponding line graph L(G). As an example, we give eχ of L(G1) from Figure 11. The edge-degrees of G1and the vertex-degrees of L(G1) are shown in Figure 17. The degree of an edge is equal to the number of adjacent edges.
Figure 17. The edge-degrees in G1and the vertex-degrees in L(G1).
| eχ(G1)= |  |
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 G1.
