This study computationally explores all possible three-node enzyme network topologies to identify those capable of achieving adaptation, a critical biological behavior where a system responds to a stimulus and returns to its pre-stimulus state. The authors found that only two core topologies emerge as robust solutions: a negative feedback loop with a buffering node (NFBLB) and an incoherent feedforward loop with a proportioner node (IFFLP). Minimal circuits containing these topologies are sufficient to achieve adaptation within certain parameter ranges. More complex circuits that robustly perform adaptation all contain at least one of these core topologies. This analysis yields a design table highlighting a finite set of adaptive circuits, suggesting that despite the diversity of biochemical networks, only a limited set of core topologies can execute specific functions. These findings provide a framework for functionally classifying complex natural networks and guide the engineering of biological circuits.This study computationally explores all possible three-node enzyme network topologies to identify those capable of achieving adaptation, a critical biological behavior where a system responds to a stimulus and returns to its pre-stimulus state. The authors found that only two core topologies emerge as robust solutions: a negative feedback loop with a buffering node (NFBLB) and an incoherent feedforward loop with a proportioner node (IFFLP). Minimal circuits containing these topologies are sufficient to achieve adaptation within certain parameter ranges. More complex circuits that robustly perform adaptation all contain at least one of these core topologies. This analysis yields a design table highlighting a finite set of adaptive circuits, suggesting that despite the diversity of biochemical networks, only a limited set of core topologies can execute specific functions. These findings provide a framework for functionally classifying complex natural networks and guide the engineering of biological circuits.