I am trying to understand how to model multiple graphs. To make that concrete, I have two distinct graphs $\{V_1, E_1\}$ and $\{V_2, E_2\}$ where $V_i$ and $E_i$ are the node sets and the edge lists respectively. The two types of nodes are qualitatively different as are the nature of the edges.
I also have a third type of outgoing edges from nodes in $V_1$ to $V_2$.
I am not entirely sure how to model this situation, inasmuch as, to my understanding it is neither a Cartesian nor a tensor product of graphs. Any suggestions of how to model this situation will be greatly appreciated.