The standard (Hurwitz-Reiter) Mechanism Design framework requires that agents broadcast their messages to a central authority that subsequently determines allocation (and tax/subsidies) for each user. We consider a setting where agents can only communicate messages to their neighbors defined by a given communication graph. As a result, allocation and tax functions for each user can only depend on local neighborhood messages. This gives rise to a new, distributed, class of mechanisms. In this paper we propose such a mechanism for the problem of rate allocation over a network with unicast transmission. The proposed mechanism is distributed, it fully implements the optimal allocation in Nash equilibria (ie, there are no extraneous equilibria), is individually rational and weak budget balanced. The message space dimension of the proposed mechanism grows linearly with the number of agents in the network.