Let $G = (V, E, D)$ be a simple graph, where $$D = \{(\{v_1, v_2\}, V^\prime) \mid \{v_1, v_2\} \in E \mbox{ and } V^\prime \subseteq V \setminus \{v_1, v_2\}\} \enspace ,$$ that is, the set of dependencies of the edges. What I mean with dependencies is that, if a vertex $v \in V$ is to be removed from the graph, not only will the edges containing $v$ be removed from $E$, but also those with $v$ in their dependencies $V^\prime$.
My question is: is there an easier way to model this? Maybe a hypergraph?
From a programming perspective it might be more usefull to save the edges depending on $V$ somewhere inside a class "Vertex". This may simply be done with by using a set containing the edges. That way you do not need to iterate over every edge when removing a vertex.