Finding common intersections in all Pathfinding solution

Sorry for the title gore, didn’t know the best way to phrase it.

So what I am trying to do is have my Guard AI find good points to cut off the player from his goal. The environment is an interior office building so these good points are defined as places where multiple hallways converge. My thinking of how to do this is given point a and b, get all possible paths and return the points where the paths intersect the most. Is there a way to do this? Sorry I couldn’t be more clear.