We prove that the modular communication complexity of the undirected graph connectivity problem UCONN equals Theta(n), in contrast to the well-known Theta(n*log n) bound in the deterministic case, and to the Omega(n*loglog n) lower bound in the nondeterministic case, recently proved by Raz and Spieker. We obtain our result by combining M"obius function techniques due to Lovasz and Saxe with rank and projection reduction arguments.