In addition to driving circular flow in ring-like circuits, complex-valued coupling can enable excitons to be directed along specific paths in branched circuits. To demonstrate this capability, we designed a model of branched circuits with two paths of linear chromophores originating from a central circular chromophore. This circuit is illustrated in Fig. . A Hamiltonian describing this system is given by, Note that a full delocalization across the circular and all the linear chromophores in the activated path (both solid and dashed lines) can be achieved by aligning the linear molecules parallel to each other.