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In operational P2P networks, an overlay topology needs to be constructed on the top of IP networks. Existing methods for the construction have limited self organizing behavior and some security problems. In this paper, the authors propose an algorithm of two parameters to construct a scale free topology for P2P networks in a self organizing manner. The emergence of scale free topologies from the algorithm is verified in both analytical and numerical ways. In addition, they demonstrate how P2P networks can benefit from the constructed topologies in terms of searching efficiency.
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