Graph matching is important for a wide variety of applications in different domains such as social network analysis and knowledge discovery. Despite extensive research over the last few decades, graph matching is still challenging particularly when it comes with new conditions and constraints. In this paper, we focus on a new class of graph matching, in which each node can accept multiple labels instead of one. In particular, we address the problem of finding the top-k nodes of a data graph which best match a labeled query node from a given pattern graph. We firstly prove this to be an NP-Complete problem. Then, to address this issue and improve the scalability of our approach, we introduce a more flexible graph simulation, namely surjective simulation. This new graph simulation reduces the unnecessary complexity that is due to the unnecessary constraints imposed by the existing definitions while achieving high-quality matching results. In addition, our approach is associated with an early stop strategy to further boost the performance. To approximate the maximum size of a simulation, our approach utilizes Metropolis Hastings algorithm and ranks the top-k matches after computing the set of surjective simulations. The experimental results over social network graphs demonstrate the efficiency of the proposed approach and superiority over existing approaches.