Self-referentially defined graph structures It is possible to define graphs $G$ such that whether an edge exists between two vertices $v_1$ and $v_2$ depends on non-local properties of $G$. 

In particular, I am interested in directed graphs where an edge $(v_1, g(v_1, w))$  exists for each leaf vertex $w$ that is reachable from $f(v_1)$. Here, $f$ maps vertices to vertices, $g$ maps pairs of vertices to vertices.

Is there research on data structures and algorithms for working with such self-referentially defined graph structures?
"Dangerous reference graphs and semantic paradoxes", Rabern, Rabern &amp; Macauley, Journal of Philosophical Logic.Here

http://philpapers.org/rec/RABDRG