Event argument extraction is critical to various natural language processing tasks for providing structured information. Existing works usually extract the event arguments one by one, and mostly neglect to build dependency information among event argument roles, especially from the perspective of event structure. Such an approach hinders the model from learning the interactions between different roles. In this paper, we raise our research question: How to adequately model dependencies between different roles for better performance? To this end, we propose an intra-event and inter-event dependency-aware graph network, which uses the event structure as the fundamental unit to construct dependencies between roles. Specifically, we first utilize the dense intra-event graph to construct role dependencies within events, and then construct dependencies between events by retrieving similar events of the current event through the retrieval module. To further optimize dependency information and event representation, we propose a dependency interaction module and two auxiliary tasks to improve the extraction ability of the model in different scenarios. Experimental results on the ACE05, RAMS, and WikiEvents datasets show the great advantages of our proposed approach.