  We consider quantum excitation energy transport (EET) in a network of
two-state nodes in the Markovian approximation by employing the Lindblad
formulation. We find that EET from an initial site, where the excitation is
inserted to the sink, is generally inefficient due to the inhibition of
transport by localization of the excitation wave packet in a symmetric,
fully-connected network. We demonstrate that the EET efficiency can be
significantly increased up to %100 by perturbing hopping transport between the
initial node and the one connected directly to the sink, while the rate of
energy transport is highest at a finite value of the hopping parameter. We also
show that prohibiting hopping between the other nodes which are not directly
linked to the sink does not improve the efficiency. We show that external
dephasing noise in the network plays a constructive role for EET in the
presence of localization in the network, while in the absence of localization
it reduces the efficiency of EET.
