The doxygen manual for graphs and diagrams lists, which kind of graphs could be created. I wasn't able to find a graph, like the one you are looking for, in that list.
The manual also states:
Warning: When you have a very large class hierarchy where many classes derive from a common base class, the resulting image may become too big to handle for some browsers.
My feeling tells me that your intended functionality, for e.g. a class like String, would go beyond the scope of any usefull usage. However my feeling might be wrong, but I'm inclined to say it's impossible, at least yet.