First and most tangential of all, the
abc (abstract base class) module is the Pythonic way to define abstract classes, though I don't believe it changes anything with respect to the question.
Now my question is: can I do something like this?
I don't think so, since there is no inheritance between Advanced and Graph, no implementation of AbstractGraph's methods will exist on Advanced. If Advanced inherited from Graph instead, that would work fine, since there would be an implementation of AbstractGraph's methods in the tree. Otherwise, Advanced itself needs to implement AbstractGraph.
I don't know quite what you're trying to do here, but in many cases composition (ie. Advanced holds an instance of AbstractGraph as a property, instead of is one itself) is a more sensible pattern than multiple inheritance, and it sounds like that might be the case here.
It also might be worth reminding that Python is a dynamically typed language where 'duck typing' is the idiomatic way to handle 'interfaces' in many / most cases. So unless you are actually intending to inherit implementations, the inheritance might actually be holding you back here. 'Interfaces' are *required* in strongly typed languages, because otherwise there would be no binding for the method signature to call, but this is not something you need to deal with in Python where the methods are bound to the instance, not the type of the reference to it a la Java.