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That was fun!  I played as both Alice and Bob.  I liked the steps of play and counter-play.  Not sure that the underlying mathematical structure is rich enough to support a full game (although I've not looked up shannon's results, so if the question of whether A or B wins is NP-complete, then maybe it is!).  My immediate thought is that this could be great as a strategic layer to some other game, so that even if you know what the optimal Bob-move is you still have to weigh up whether that's the connection you want to try and cut?  Just spitballing.

I like the aesthetics, but it's a pity to have to scroll around to see the whole network.  Nice game, anon!