I am not sure to understand 100%, but it seems to me that your processor must be able to travel in time if you want to make such computation.
I mean, if the computational graph is cyclic (let say the simplest case, with 2 nodes), you need the result of operation 1 in order to compute operation 2, in order to compute operation 1. So you need the result of operation 1 in order to compute its own result.
Otherwise, you think about a time decomposition (so you need the result at time 0 for the result at time 1) but then the graph is acyclic