Architecturing method inheritance / hiding method in child class

I am trying to write some Deterministic Finite Automaton related algorithms. So the obvious start is to define the entities: DFA, State and Edges. However, I though since the DFA is a kind of graph I should have basic classes Graph, Node and Edge each implementing IGraph, INode and IEdge. And then have DFA and State extend Graph and Node.

So the stripped down code of Graph is:

class Graph
{
    //...
    public void addNode(INode node)
    {
        //...
    }
    //... 
}

Now the main difference between State and Node is that State adds properties isFinalState and isStartingState to Node. So I want State objects to be added to the DFA not the Node objects through Graph's addNode() method.

I thought I can override and make this method private in DFA and have defined a new method addState() which will accept State objects. But reducing the visibility of parent class members in derived class is not allowed in Java.

So what is the standard solution / approach followed in such scenarios. Or am I thinking this all wrong?