Using a classical master equation that describes energy transfer over a given lattice, we explore how energy transfer efficiency along with the photon capturing ability depends on network connectivity, on transfer rates, and on volume fractions-the numbers and relative ratio of fluorescence chromophore components, e.g., donor (D), acceptor (A), and bridge (B) chromophores. For a one-dimensional AD array, the exact analytical expression (derived in Appendix A) for efficiency shows a steep increase with a D-to-A transfer rate when a spontaneous decay is sufficiently slow. This result implies that the introduction of B chromophores can be a useful method for improving efficiency for a two-component AD system with inefficient D-to-A transfer and slow spontaneous decay. Analysis of this one-dimensional system can be extended to higher-dimensional systems with chromophores arranged in structures such as a helical or stacked-disk rod, which models the self-assembling monomers of the tobacco mosaic virus coat protein. For the stacked-disk rod, we observe the following: (1) With spacings between sites fixed, a staggered conformation is more efficient than an eclipsed conformation. (2) For a given ratio of A and D chromophores, the uniform distribution of acceptors that minimizes the mean first passage time to acceptors is a key point to designing the optimal network for a donor-acceptor system with a relatively small D-to-A transfer rate. (3) For a three-component ABD system with a large B-to-A transfer rate, a key design strategy is to increase the number of the pathways in accordance with the directional energy flow from D to B to A chromophores. These conclusions are consistent with the experimental findings reported by Francis, Fleming, and their co-workers and suggest that synthetic architectures of self-assembling supermolecules and the distributions of AD or ABD chromophore components can be optimized for efficient light-harvesting energy transfer.