This is a hard question to put into words. Please be patient with me.
In graph theory, we have a set $V$ of vertices and a set $E$ of edges. The elements of $E$ are usually 2-tuples, or something similar, which denotes the connection between two elements of $V$. It doesn't matter what the objects in $V$ actually 'are', they could be numbers or sets or groups or whatever. The graph is what's important.
Meanwhile, over in systems of differential equations, we can have a bunch of variables that depend on the current states of one another to predict their future states, like the Lorenz system. If we think about those stateful objects as the elements of $V$, then the elements of $E$ might actually be functions that take elements of $V$ as their arguments -- and if a function $e \in E$ exists that depends on $v_1, v_2 \in V$, then we could use that as our "edge" to link those two variables together, instead of just a 2-tuple.
My question to you is: What kind of field am I talking about? What do I read, or what do I Google? I'm sure someone has a name for this, but I just have no idea where to even begin.