Thanks for your comment. I have two questions. 1) Is the union (graph_1, graph_2) is supposed to equal union (graph_2, graph_1) ?.
Yes. Union is a commutative operation.
2) I want to ask if the Covariance theory [1] is applicable to solve the problem of graph properties. In the below example, I want to explain how I will apply the theory: G1 is a graph representing the connection between students. So G1's vertex_property is *student*. G2 is a graph representing the connection between professors. So G2's vertex_property is *professor*. Since both *student* and *professor* are inside *people*, I can use *people* as Union_Graph 's vertex_property.
I don't think that this will work particularly well. It's probably easier to assume that vertex and edge properties are either the same type or completely unrelated. Andrew Sutton andrew.n.sutton@gmail.com