The equivalence relation—a qualitative discussion

Atoms exist in real space and they are defined by a partitioning of real space. The notion of structure is abstract and it is defined through a partitioning of control space in a manner determined by the behaviour of the system in real space. In this way structure is associated with an open region of nuclear configuration space and necessarily satisfies the condition that it be a generic property of the system. 

This is the general idea behind the definition of a stable structure—an open region of nuclear configuration space, all points of which have the same molecular graph. A molecular graph is determined by the gradient vector 

---