Efficient structure of noisy communication networks

In the canonical network model, the connections model, only three specific network structures are generically efficient: complete, empty, and star networks. This renders many plausible network structures inefficient. We show that requiring robustness with respect to stochastic transmission failures rehabilitates incomplete, circular network structures. Specifically, we show that near the "bifurcation" where both star and complete network are efficient in the standard connections model, star and complete network are generally inefficient as transmission failures become possible. As for four-player networks, we additionally show that the circle network is uniquely efficient and robust near this bifurcation.