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Future wireless networks need to support the increasing demands for high data rates and improved coverage. One promising solution is sectorization, where an infrastructure node (e.g., a base station) is equipped with multiple sectors employing directional communication. Although the concept of sectorization is not new, it is critical to fully understand the potential of sectorized networks, such as the rate gain achieved when multiple sectors can be simultaneously activated. In this paper, we focus on sectorized wireless networks, where sectorized infrastructure nodes with beam-steering capabilities form a multi-hop mesh network for data forwarding and routing. We present a sectorized node model and characterize the capacity region of these sectorized networks. We define the flow extension ratio and the corresponding sectorization gain, which quantitatively measure the performance gain introduced by node sectorization as a function of the network flow. Our objective is to find the optimal sectorization of each node that achieves the maximum flow extension ratio, and thus the sectorization gain. Towards this goal, we formulate the corresponding optimization problem and develop an efficient distributed algorithm that obtains the node sectorization under a given network flow with an approximation ratio of 2/3. Through extensive simulations, we evaluate the sectorization gain and the performance of the proposed algorithm in various network scenarios with varying network flows. The simulation results show that the approximate sectorization gain increases sublinearly as a function of the number of sectors per node.