The paper introduces a new class of consensus protocols to reach an agreement in networks of agents with discrete time dynamics. In order to guarantee the convergence of the proposed algorithms, some general results are proved in the framework of non-negative matrix theory. Moreover, we characterize the set of the consensus protocols and we specify the algorithm that each agent has to employ. Furthermore, we show that in the case of balanced graphs, the agents can apply the consensus protocols by a decentralized and scalable computation. The convergence properties are studied by a set of tests that show the good performance of the proposed algorithm for different network topologies, even in the cases in which the standard protocols do not exhibit satisfying performances. In particular, a rigorous theoretical analysis of the proposed protocol convergence for networks with ring topology is provided and compared with the standard algorithm. (C) 2015 Elsevier Ltd. All rights reserved.