Nice battle concept.
Is enemy get any stronger at later point? I got to level 42 and I think monster is not get any stronger for a while so I just quit.
The main mechanic is very interesting but I have 3 problem with it.
1. you can add any edge but only have 2 choice when remove (I don't know how the removable node is determine) and most of the time 1 choice make my graph return to previous 2 level, other choice make my graph worse. at level 42 my main graph loop look almost identical to my graph at level 6 (which only use 3 node loop "Attack-Attack-Heal").
2. there are no incentive to do big loop, small loop is much more efficient and easier to optimize.
3. player rarely have a choice in the battle, because you have to remove edge every 2 level (and I can't even choice the edge that I want to remove) it hard to make a graph with 2 out-node where both node make a useful loop, and without a choice sometime attack even sync with an enemy's defend turn and make that run unplayable.
Anyway, nice job on making the game in 2 days, I know it hard to balance the game within this time frame.