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This paper considers the problem of consensus of multiple agents with dynamically changing interaction topologies. It is shown that a multi-agent system can achieve consensus asymptotically if the union of the directed interaction graphs is weakly connected frequently enough as the system evolves. To establish convergence condition of consensus, some new concepts and properties of graphs have been proposed and revealed. To see the strength of this new condition, some existed consensus convergence conditions have been shown to be special cases of our result.