Graph pattern matching has been widely used in large spectrum of real applications. In this context, different models along with their appropriate algorithms have been proposed. However, a major drawback on existing models is their limitation to find meaningful matches resulting in a number of failing queries. In this paper we introduce a new model for graph pattern matching allowing the relaxation of queries in order to avoid the empty-answer problem. Then we develop an efficient algorithm based on optimization strategies for computing the top-k matches according to our model. Our experimental evaluation on four real datasets demonstrates both the effectiveness and the efficiency of our approach.