  We present a theoretical analysis of the efficiency and rate of excitation
transport on a network described by a complete graph in which every site is
connected to every other. The long-time transport properties are analytically
calculated for networks of arbitrary size that are symmetric except for the
trapping site, start with a range of initial states, and are subject to
dephasing and excitation decay. Conditions for which dephasing increases
transport are identified, and optimal conditions are found for various physical
parameters. The optimal conditions demonstrate robustness and a convergence of
timescales previously observed in the context of light-harvesting complexes.
