number of vertices :  11 
number of required edges  7 
1 2 3 3 9
3 4 6 6 6
3 5 1 1 2
5 6 2 2 6
7 8 8 8 13
9 10 1 1 3
10 11 4 4 9
number of non required edges  6 
1 10 5 5 0
2 3 10 10 5
4 5 1 1 0
4 8 4 4 3
5 11 22 22 4
6 7 9 9 3
