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We present a theoretical analysis of the efficiency and rate of excitationtransport on a network described by a complete graph in which every site isconnected to every other. The long-time transport properties are analyticallycalculated for networks of arbitrary size that are symmetric except for thetrapping site, start with a range of initial states, and are subject todephasing and excitation decay. Conditions for which dephasing increasestransport are identified, and optimal conditions are found for various physicalparameters. The optimal conditions demonstrate robustness and a convergence oftimescales previously observed in the context of light-harvesting complexes.

Optimal Conditions for Environment-Assisted Quantum Transport on the Fully Connected Network