number of vertices :  7 
number of required edges  4 
1 2 4 4 12
2 3 1 1 1
4 5 5 5 10
6 7 2 2 6
number of non required edges  6 
1 5 8 8 2
1 7 7 7 6
3 4 5 5 3
3 5 9 9 0
3 7 8 8 4
5 7 9 9 1
