The concept of this game is good. I was able to beat every level by connecting the blue node to the green node though, so that would be a good thing to fix.
You could turn this into a memory/puzzle type game pretty easily if you make the 'dead' nodes the same color as the 'alive' ones. Then when the player connects a path to the green node it will either turn on or let them know there are dead nodes in the path they created. You could either show them which nodes are dead, or let them figure it out through trial and error. I think that could be really fun!