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Information propagation speed (IPS) in a multihop cognitive radio network (CRN) is an important factor that affects the network's delay performance and needs to be considered in network planning. The impact of primary user (PU) activities on IPS makes the problem of analyzing IPS in multihop CRNs very challenging and hence unsolved in existing literature. In this paper, we fill this technical void. We establish a IPS model in multihop CRNs, and compute the maximum network IPS that maximizes IPS across a network topology over an infinite plane. We reveal that the maximum network IPS is determined by the PU activity level and the placement of secondary user relay nodes. We design optimal relay placement strategies in CRNs to maximize the network IPS under different PU activity levels. The correctness of our analytical results is validated by simulations and numerical experiments.