We revisit the classic multi-agent distributed consensus problem under mild connectivity assumptions and non-uniformly bounded weights. The analysis is based on a novel application of the standard results from the non-negative matrix theory. It is a simple, yet unifying, approach that yields generalized results. We apply these results to a wide variety of linear, non-linear consensus and flocking algorithms proposed in the literature and we obtain new conditions for asymptotic consensus. Our framework is developed in both discrete and continuous time. Furthermore we extend the discussion to stochastic settings.