Optical technology has made significant contributions to the state-of-the-art for long distance communications, including high reliability, low interference, security benefits, and (most important) very high bandwidth. However, the technology has yet to be successfully exploited in the domain of tightly-coupled multicomputer systems. To successfully exploit the benefits of optical technology in a tightly-coupled multicomputer, the architectural design must reflect both the advantages of optics and the limitations of optics. This article describes a class of such architectures, based upon inverted graph topologies. We consider the physical construction of these systems, demonstrating the relevant technological components necessary to manufacture a working system. We then consider two example topologies (an inverted hypercube and an inverted mesh), illustrating their properties, including processor labeling, topological embeddings, and message routing algorithms.