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This paper proposes a distributed reputation model for open peer-to-peer networks called distributed pagerank. This model is motivated by the observation that although pagerank has already satisfied the requirements of reputation models, the centralized calculation of pagerank is incompatible with peer-to-peer networks. Distributed pagerank is a decentralized approach for calculating the pagerank of each peer by its reputation, in which the relationship between peers is introduced as the equivalent to the link between Web pages. The distributed calculation of pagerank is performed asynchronously by each peer as it communicates with the other peers. The asynchronous calculation accomplishes both demanding no extra messages for the calculation of pagerank and steadily calculating an accurate pagerank of each peer even under the dynamic topology of relationships. The result of the simulation has indicated that the calculated pagerank value of each peer converges at the original pagerank value under the static topology of relationships, which is presumable under a dynamic topology. A fully implemented application of distributed pagerank has also been presented, which supports dynamic formation of communities with reputation ranking.