With the rapid progress of the integrated nanophotonics technology, the optical neural network (ONN) architecture has been widely investigated. Although the ONN inference is fast, conventional densely connected network structures consume large amounts of power in laser sources. We propose a novel ONN design method that finds an ultrafast, energy-efficient, and accurate ONN structure. The key idea is power-aware edge pruning that derives the near-optimal numbers of edges in the entire network. Optoelectronic circuit simulation demonstrates the correct functional behavior of the ONN. Furthermore, experimental evaluations using tensor-flow show the proposed methods achieved 98.28% power reduction without significant loss of accuracy.