Quote:
Originally Posted by charlieabranches
Any aspect that you can to consider:
Isn't possible to walk all path's with 0 and 1 repetion, I concluse that because I try a lot times, but i can't prove with a formula.

Count the number of paths connected to each point. Whenever a walker approaches a point, he takes one path; he leaves by another. If a point has an even number of connected paths, it may be possible to visit (and revisit) it without reusing a path. If a point has an odd number of connected paths, the walker will be forced to reuse one.
If you consider the entrance and exit arrows to be paths, all points have an even number of connected paths except B and H. So you'll be required to reuse one path for each of those points. Your solution reuses the shortest path in both cases, and has no other repetitions. So it's the best possible result. (I think.)