I am trying to solve a problem in continuous space $\Bbb{R}^2$, however, it was previously for non-directed graphs with edges and vertices.
Now, I am trying to translate this two concepts to the continuous space. I have stated that the vertices $V$ are now any point $v\in\Bbb{R}^2$ but for the edge set $E$ I don't know how to state that $\forall v$, its valid transitions are
Any consecutive point in the state space
Is there any way I can express this? Or how can I translate the graph concepts of transitions in the real space?