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Distributed networks have attracted much attention due to their scalability and inexpensiveness as compared to traditional centralized networks. While distributed networks are appropriate to construct large-scale networks, insuring the tolerance to network-failures (ie, attacks and faults) and communication efficiency is still an unresolved issue. In this paper, we classify and evaluate the existing distributed networks based on their degree distributions. We also propose a method to construct a network based on bimodal degree distribution, which is tolerant to network-failures insuring high communication efficiency. Additionally, through computer simulations, we show that the proposed method achieves higher tolerance compared to other existing methods.