def _internal_build(self):
        """ This function assumes the self.__tree object has been setup,
            though it doesn't care how. It will then setup all python
            side data structures to be used for querying this object.
        """
        self.nodes = self.__tree.Nodes()
        self.edges = self.__tree.Edges()
        self.augmentedEdges = {}
        for key, val in self.__tree.AugmentedEdges().items():
            self.augmentedEdges[key] = list(val)
        self.root = self.__tree.Root()

        seen = set()
        self.branches = set()

        # Find all of the branching nodes in the tree, degree > 1
        # That is, they appear in more than one edge
        for e1, e2 in self.edges:
            if e1 not in seen:
                seen.add(e1)
            else:
                self.branches.add(e1)

            if e2 not in seen:
                seen.add(e2)
            else:
                self.branches.add(e2)

        # The nodes that are not branches are leaves
        self.leaves = set(self.nodes.keys()) - self.branches
        self.leaves.remove(self.root)