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Process mining is an area of research that supports discovering information about business processes from their execution event logs. One of the challenges in process mining is to deal with the increasing amount of event logs and the interconnected nature of events in organizations. This issue limits the organizations to apply process mining on a large scale. Therefore, this paper introduces and formalizes a new approach to store and retrieve event logs into/from graph databases. It defines an algorithm to compute Directly Follows Graph (DFG) inside the graph database, which shifts the heavy computation parts of process mining into the graph database. Calculating DFG in graph databases enables leveraging the graph databases' horizontal and vertical scaling capabilities to apply process mining on a large scale. We implemented this approach in Neo4j and evaluated its performance compared with some current techniques using a real log file. The result shows the possibility of using a graph database for doing process mining in organizations, and it shows the pros and cons of using this approach in practice.