Mining the frequent pattern from data set is one of the key success stories of data mining research. Currently, most of the efforts are focused on the independent data such as the items in the marketing basket. However, the objects in the real world often have close relationship with each other. How to gain the frequent pattern from these relations is the objective in this paper. We use graphs to model the relations, and select a simple type for analysis. Combining the graph-theory and algorithms to generate frequent patterns, a new structure SFP-Tree and an algorithm, which can mine these simple graphs efficiently, have been proposed. We evaluate the performance of the algorithm by experiments with synthetic datasets. The empirical results show that the SFP can do the job well. At the end of this paper, the potential improvement of SFP is mentioned.