2019 **Abstract:** A stochastic weighted averaging consensus algorithm is considered for a multi-agent system over a noisy unbalanced directed network. The convergence of the algorithm is investigated, which gives an explicit relation between the number of iterations and the closeness of the agreement, i.e., a stopping rule.

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“…Finally, we conclude this paper in Section 5. The preliminary versions of this study were presented at conferences [14], [15], where unweighted graphs are considered. On the other hand, the present paper deals with general weighted graphs, where it is shown that the stopping rules can be basically the same, and thus introducing the weights does not affect the computational complexity of the consensus algorithms.…”

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“…Finally, we conclude this paper in Section 5. The preliminary versions of this study were presented at conferences [14], [15], where unweighted graphs are considered. On the other hand, the present paper deals with general weighted graphs, where it is shown that the stopping rules can be basically the same, and thus introducing the weights does not affect the computational complexity of the consensus algorithms.…”