Is a node a node and an edge an edge?

It so happens that in simple cases, graphs of structured assortments of defined and similar data, nodes and edges may be closely defined.   In graphs of more complex objects, in which between nodes a relationship of one kind may describe something different than another, edges take on 'character'.

For example, consider two node objects A and B.   Let us say that A contains a flag bit and also B contains a flag bit.   
Let us say that each also contain a scalar value.
Nodes connecting these of objects could compare flag truth values, greater than/equality of the scalar values, a true logical statement of the flag bits in A relating to the value of B, or other compact information convergence.