In recent years, the popularity of graph databases has grown rapidly. This paper focuses on single-graph as an effective model to represent information and its related graph mining techniques. In frequent pattern mining in a single-graph setting, there are two main problems: support measure and search scheme. In this paper, we propose a novel framework for constructing support measures that brings together existing minimum-image-based and overlap-graph-based support measures. Our framework is built on the concept of occurrence / instance hypergraphs. Based on that, we present two new support measures: minimum instance (MI) measure and minimum vertex cover (MVC) measure, that combine the advantages of existing measures. In particular, we show that the existing minimum-image-based support measure is an upper bound of the MI measure, which is also linear-time computable and results in counts that are close to number of instances of a pattern. Although the MVC measure is NP-hard, it can be approximated to a constant factor in polynomial time. We also provide polynomial-time relaxations for both measures and bounding theorems for all presented support measures in the hypergraph setting. We further show that the hypergraph-based framework can unify all support measures studied in this paper. This framework is also flexible in that more variants of support measures can be defined and profiled in it.