In this paper, we consider Harary graphs as candidate solutions for the design of a physical network topology that achieves a high level of reliability using unreliable network elements. Our network model, which is motivated by the use of all-optical networks for high-reliability applications, is one in which nodes are invulnerable and links are subject to failure in a statistically independent fashion. Our reliability metrics are the all-terminal connectedness measure and the less commonly considered two-terminal connectedness measure. We compare in the low and high stress regimes common commercial architectures designed for all-terminal reliability in the low stress regime with the Harary graph architecture. We focus on Harary graphs as candidate topologies, as they have been shown to possess attractive reliability properties, and we derive new results for this family of graphs.