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Peer-to-peer (P2P) networks often demand scalability, low communication latency among nodes, and low systemwide overhead. For scalability, a node maintains partial states of a P2P network and connects to a few nodes. For fast communication, a P2P network intends to reduce the communication latency between any two nodes as much as possible. With regard to a low systemwide overhead, a P2P network minimizes its traffic in maintaining its performance efficiency and functional correctness. In this paper, we present a novel tree-based P2P network with low communication delay and low systemwide overhead. The merits of our tree-based network include 1) a tree-shaped P2P network, which guarantees that the degree of a node is constant in probability, regardless of the system size (the network diameter in our tree-based network increases logarithmically with an increase in the system size, and in particular, given a physical network with a power-law latency expansion property, we show that the diameter of our tree network is constant), and 2) provable performance guarantees. We evaluate our proposal by a rigorous performance analysis, and we validate this by extensive simulations.