Sharing intentions is crucial for efficient cooperation in communication-enabled multi-agent reinforcement learning. Recent work applies static or undirected graphs to determine the order of interaction. However, the static graph is not general for complex cooperative tasks, and the parallel message-passing update in the undirected graph with cycles cannot guarantee convergence. To solve this problem, we propose Deep Hierarchical Communication Graph (DHCG) to learn the dependency relationships between agents based on their messages. The relationships are formulated as directed acyclic graphs (DAGs), where the selection of the proper topology is viewed as an action and trained in an end-to-end fashion. To eliminate the cycles in the graph, we apply an acyclicity constraint as intrinsic rewards and then project the graph in the admissible solution set of DAGs. As a result, DHCG removes redundant communication edges for cost improvement and guarantees convergence. To show the effectiveness of the learned graphs, we propose policy-based and value-based DHCG. Policy-based DHCG factorizes the joint policy in an auto-regressive manner, and value-based DHCG factorizes the joint value function to individual value functions and pairwise payoff functions. Empirical results show that our method improves performance across various cooperative multi-agent tasks, including Predator-Prey, Multi-Agent Coordination Challenge, and StarCraft Multi-Agent Challenge.