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The Fibonacci numbers are the numbers defined by the linear recurrence equation, in which each subsequent number is the sum of the previous two. In this paper, we propose Fibonacci networks using Fibonacci numbers. The analyticai expressions involving degree distribution, average path lengh and mean first passage time are obtained. This kind of networks exhibits the smail-world characteristic and follows the exponential distribution. Our proposed models would provide the vaiuable insights into the deterministicaily delayed growing networks.