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In this note, we discuss the problem of consensus finding in communicationnetworks of agents with dynamically switching topologies. In particular, weconsider the case of directed networks with unbalanced matrices ofcommunication rates. We formulate sufficient conditions for consensus findingin terms of strong connectivity of the underlying directed graphs and provethat, given these conditions, consensus is found asymptotically. Moreover, weshow that this consensus is an emergent property of the system, being encodedin its dynamics and not just an invariant of its initial configuration.

A Note on the Consensus Finding Problem in Communication Networks with Switching Topologies