Process mining is a research area focusing on the design of algorithms that can automatically provide insights into business processes. Among the most popular algorithms are those for automated process discovery, which have the ultimate goal to generate a process model that summarizes the behavior recorded in an event log. Past research had the aim to improve process discovery algorithms irrespective of the characteristics of the input log. In this paper, we take a step back and investigate the connection between measures capturing characteristics of the input event log and the quality of the discovered process models. To this end, we review the state-of-the-art process complexity measures, propose a new process complexity measure based on graph entropy, and analyze this set of complexity measures on an extensive collection of event logs and corresponding automatically discovered process models. Our analysis shows that many process complexity measures correlate with the quality of the discovered process models, demonstrating the potential of using complexity measures as predictors of process model quality. This finding is important for process mining research, as it highlights that not only algorithms, but also connections between input data and output quality should be studied.
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