This is super cool to play around with and really illustrative.

One thing I noticed about the game is that I was able to "solve" some puzzles by accident when I went to erase a set of edges at once. I guess at some step during removing edges the puzzle was solved, but the game both registered the puzzle was complete AND applied the rest of the erasures afterwards. This lead to me moving to the next screen when the network didn't satisfy the requirement, so I didn't get to see the actual solution.

I would recommend changing the game so that it either waits for the user to let go of the mouse button (ie all the edits are applied before checking for correctness), or ignoring edits for a set period of time after the solution is found.