Figure 5. (a), (b) Sample generalized Toffoli gate with corresponding interaction graph. (c), (d) Cuccaro adder with interaction graph, M and N are three qubit gate blocks. Some circuits, such as the CNU circuit and Cuccaro Adder have clusters of qubits that interact with one another. These clusters can be identified by finding the cycles in the interaction graph. We have identified the cycles here with colored edges.