We study a wireless full-duplex network with imperfect interference cancellation and solve the routing and power allocation problem in this network. We use a model that focuses on the effects of full-duplex by including residual self-interference and one hop interference while other interfering signals are considered negligible in comparison. We first solve the optimal power allocation for a fixed route. We then propose a priority-first search algorithm to find the joint route and power allocation to maximize throughput. The algorithm proposed has a non decomposable priority metric, but is efficiently evaluated by our solution for a fixed route. We analyze the performance of our solution in a more realistic model by deriving bounds between optimal solutions in both models. Through simulations we show that, even with imperfect interference cancellation, full-duplex achieves a higher throughput than half-duplex or direct transmission for moderate transmission power.