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