Not bad! It's a nice territory-capture game with a simple mechanic and some fun strategies.
The first time couple of times I played were a little tough—a lot of back-and-forth, which taught me some useful strategies (e.g. decomposing my nodes into separate connected components, arranged such that the farthest ones from the enemy had multiple nodes primed to connect back up). However, when I came back to it the next day, I found it far easier—almost too easy, even with the "hard" AI setting.
Btw, how does the AI work? Are you using minimax just on the edge nodes to keep the game tree manageable, or something else? If the former, that might explain the lack of more subtle strategy; the AI only seems to care about capturing more territory, and very little about damage control. I can imagine that, if you didn't, it would be tough to squeeze out decent performance after a few ply! I also seem to remember you had a few different "styles" of AI in a previous version, which I imagine meant swapping out the utility functions?
I saw a few bugs that have been commented on already, e.g. the incorrect count of AI territory and that the green player doesn't work on large maps with teams mode (nor does it move in free-for-all).
One other, very minor thing that would improve the interface would be a sans-serif font on the main game interface. (At first, I thought it was because I'm on a Mac and you're using a non-system font that wasn't downloaded, but Inspector shows no fonts being set.)
Great work in progress. Really looking forward to seeing where this goes!