<p>Because most data in the real world can be represented in graph structures, graph mining is essential in many fields. In recent decades, research on algorithms for mining frequent subgraphs in graph databases has matured. In addition to frequent patterns, periodic and closed patterns are important in real life. However, the definition of periodic patterns in the precedent study is rigorous and has certain limitations, so that many approximate periodic patterns cannot be mined. Thus, based on the study of periodic patterns in itemset databases, we define periodic frequent subgraphs (PFSs) in dynamic graphs using the three measures: average periodicity, maximum periodicity, and minimum periodicity. The task of PFS mining is to discover all the PFSs in a given database. We propose the PFS Miner (PFSM) algorithm to realize this task. In addition, we propose closed PFSs (CPFSs) and the corresponding mining algorithm named CPFS Miner (CPFSM) to make the excavated periodic frequent patterns more concise. Finally, we conduct experiments on real datasets to analyze the performance of the algorithms. The experimental results indicate that the PFSM algorithm can mine meaningful periodic frequent patterns and CPFSM can mine closed periodic frequent patterns with good efficiency and performance.</p>