Let $N$ be the signal graph representation network of the system function (in rationale form) of a discrete-time LTI system. For a network $N$ with no loops, the impulse response is no longer than the total number of delay elements in the network. From this, we conclude that if a network has no loops, then the system function has only zeros (except for poles at $z = 0$), and the number of zeros can be no more than the number of delay elements in the network.
Q: Why can the number of zeros be no more than the number of delay elements in the network?