Reinforcement learning (RL) algorithms have been widely applied in traffic signal studies. There are, however, several problems in jointly controlling traffic lights for a large transportation network. First, the action space exponentially explodes as the number of intersections to be jointly controlled increases. Although a multi-agent RL algorithm has been used to solve the curse of dimensionality, this neither guaranteed a global optimum, nor could it break the ties between joint actions. The problem was circumvented by revising the output structure of a deep Q-network (DQN) within the framework of a single-agent RL algorithm. Second, when mapping traffic states into an action value, it is difficult to consider spatio-temporal correlations over a large transportation network. A deep graph Q-network (DGQN) was devised to efficiently accommodate spatio-temporal dependencies on a large scale. Finally, training a RL model to jointly control traffic lights in a large transportation network requires much time to converge. An asynchronous update methodology was devised for a DGQN to quickly reach an optimal policy. Using these three remedies, a DGQN succeeded in jointly controlling the traffic lights in a large transportation network in Seoul. This approach outperformed other state-of-the-art RL algorithms as well as an actual fixed-signal operation.