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In this paper, we propose the C1-networks, including the complete C1-networks and the incomplete C1-networks, which evolved from the B-networks. The main difference between the complete C1-network and the B-network is their connecting pattern between the stages. The available MINs to date are almost all restricted by the port number in the power of 2. The C1-network is not under the control of this restriction, hence, good flexibility is obtained. In addition, the single-buffer performance model is developed and evaluated, and some results are given.