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While routing in wireless networks has been studied extensively, existing protocols are typically designed for a specific set of network conditions and so cannot accommodate any drastic changes in those conditions. For instance, protocols designed for connected networks cannot be easily applied to disconnected networks. In this paper, we develop a distributed routing strategy based on deep reinforcement learning that generalizes to diverse traffic patterns, congestion levels, network connectivity, and link dynamics. We make the following key innovations in our design: (i) the use of relational features as inputs to the deep neural network approximating the decision space, which enables our algorithm to generalize to diverse network conditions, (ii) the use of packet-centric decisions to transform the routing problem into an episodic task by viewing packets, rather than wireless devices, as reinforcement learning agents, which provides a natural way to propagate and model rewards accurately during learning, and (iii) the use of extended-time actions to model the time spent by a packet waiting in a queue, which reduces the amount of training data needed and allows the learning algorithm to converge more quickly. We evaluate our routing algorithm using a packet-level simulator and show that the policy our algorithm learns during training is able to generalize to larger and more congested networks, different topologies, and diverse link dynamics. Our algorithm outperforms shortest path and backpressure routing with respect to packets delivered and delay per packet.