Semi-supervised clustering has recently received a lot of attention in the literature, which aims to improve the clustering performance with limited supervision. Most existing semi-supervised clustering studies assume that the data is represented in a vector space, e.g., text and relational data. When the data objects have complex structures, e.g., proteins and chemical compounds, those semi-supervised clustering methods are not directly applicable to clustering such graph objects. In this paper, we study the problem of semi-supervised clustering of data objects which are represented as graphs. The supervision information is in the form of pairwise constraints of must-links and cannot-links. As there is no predefined feature set for the graph objects, we propose to use discriminative subgraph patterns as the features. We design an objective function which incorporates the constraints to guide the subgraph feature mining and selection process. We derive an upper bound of the objective function based on which, a branch-and-bound algorithm is proposed to speedup subgraph mining. We also introduce a redundancy measure into the feature selection process in order to reduce the redundancy in the feature set. When the graph objects are represented in the vector space of the discriminative subgraph features, we use semi-supervised kernel K-means to cluster all graph objects. Experimental results on real-world protein datasets demonstrate that the constraint information can effectively guide the feature selection and clustering process and achieve satisfactory clustering performance.