The connectivity of distributed networked multi-robot systems is a crucial operational specification, since the involved robots interact/communicate locally only with their immediate neighbors. Thus, in this work, we propose a distributed algorithm to estimate the algebraic connectivity of the underlying communication graph, which stands as a valid connectivity metric. Our method establishes robustness and fast convergence properties that can be adjusted independently via the appropriate selection of certain design parameters. Finally, we confirm the theoretical findings through simulated paradigms and verify the superiority of our method against a well-established solution of the related literature.