Multihop network has been considered as a breakthrough frontier to enhance the coverage of wireless network. Spectrum-sharing is an efficient technique to enhance the utilization of the limited radio frequency bandwidth. In this paper, we therefore consider the extension of multihop network to cognitive radio networks with the spectrum sharing approach. In particular, we investigate the cognitive multihop networks in the presence of multiple licensed transmitters and receivers. Under the stringent power constraint imposed by the licensed users, we derive the closed-form and asymptotic expressions for the outage probability over Nakagami-m fading channels. The tractable closed-form expressions reveal the impact of important network parameters such as the fading severity parameters of the unlicensed network, the number of licensed users, the peak interference power imposed by the licensed receivers, the interference power from licensed transmitters. A significant observation corroborated by our study shows that the cognitive multihop networks benefit both cognitive radio and multihop networks for improving the coverage extension and frequency spectrum utilization.