ftl-like map generator

Hey guys. i am trying to do ftl-like map generator. I can generate nodes randomly and define start-exit as you can see in image. But i couldn’t establish meaningful paths. I try to chose closest nodes to move, but dead end occurs. (cannot even reach exit.) I try to make circle, but not as required again. Can you suggest me a way? I want to create ftl-like movement. Thanks.

One way is to do delaunay triangulation of the points to get a graph where all nodes are gauranteed to be connected. Then you can remove edges in the graph one by one, checking that each removal does not affect the ability to reach the start node, by using pathfinding.