When I drag a GraphML file from a file browser onto yEd or double-click a GraphML file in a file browser, the "save as" path and the "export" path do change to the thus opened file's directory. If this is not the case for you, please start a new thread with a step-by-step description of what you are doing, what you expect to happen, and what actually happens. Please also include the name and version of the operating system on which you are running yEd and the version of the Java runtime environment of which you are running yEd.
Moreover, my original answer meant that yEd did not offer a way for users to change its behavior in this regard. Of course, it was possible for us to implement a different behavior for yEd (which we did).