Knowledge graph is a way of structuring information in graph form, by representing entities as nodes and relationships between entities as edges. A knowledge graph often consists of large amount of facts in real-world which can be used in supporting many analytical tasks, e.g., exceptional facts discovery and fact check of claims. In this work, we study a core-based top-k frequent pattern discovery problem which is frequently used as a subroutine in analyzing knowledge graphs. The main challenge of the problem is search space of the candidate patterns is exponential to the combinations of the nodes and edges in the knowledge graph.To reduce the search space, we devise a novel computation framework FastPat with a suite of optimizations. First, we devise a meta-index, which can be used to avoid generating invalid candidate patterns. Second, we propose an upper bound of the frequency score (i.e., MNI) of the candidate pattern that prunes unqualified candidates earlier and prioritize the enumeration order of the patterns. Lastly, we design a join-based approach to compute the MNI of candidate pattern efficiently. We conduct extensive experimental studies in real-world datasets to verify the superiority of our proposed method over the baselines. We also demonstrate the utility of the discovered frequent patterns by a case study in COVID-19 knowledge graph.