I'm not too familiar with pointers, but would I changeI would think the first option is better, changing the Graph member of Movie to be a pointer.
toCode:///The private graph for the Kevin Bacon Problem mutable Graph actorGraph;
If I do that, which I'm sure is wrong, then the error in the Graph.h file went away but I now have errors in my Movie.cpp class in the function actorConnections and printPath.Code:mutable Graph *actorGraph;