Somarakis, ChristoforosIn this report, we revisit the classical multi-agent distributed consensus problem under the dropping of the general assumption that the existence of a connection between agent implies weights uniformly bounded away from zero. We reformulate and study the problem by establishing global convergence results both in discrete and continuous time, under fixed, switching and random topologies.processes on graphsconsensusLinear Processes Under Vanishing Communications - The Consensus ProblemTechnical Report