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Navigating mobile robots along time-efficient and collision-free paths in crowds is still an open and challenging problem. The key is to build a profound understanding of the crowd for mobile robots, which is the basis of a proactive and foresighted policy. However, since the interaction mechanisms among pedestrians are complex and sophisticated, it is difficult to describe and model them accurately. For the excellent approximation capability of deep neural networks, deep reinforcement learning is a promising solution to the problem. However, current model-free learning-based approaches in crowd navigation always neglect planning and still lead to reactive collision avoidance policies and shortsighted behaviors. Meanwhile, most model-based learning-based approaches are based on state values, imposing a substantial computational burden. To address these problems, we propose a graph-based deep …