In order to enable experimentations and simulations of bigraphs, we need an implementation of their dynamic. In this paper, we tackle the matching issue of this task. We present a solution based on an investigation on graph matching. We propose to simulate a bigraphical reactive system (i.e., bigraphs with a set of reaction rules that allow their rewriting) with a graph transformation system. First, we translate a bigraph to a ranked graph. This translation is ensured by defining a faithful functor that allows to move from the bigraph category to the ranked graph category. Then, we show that reaction rules can be simulated with graph rules. Hence, we provide a formal basis allowing to execute bigraph transformations by simulating their translation aiming to use well-established and efficient graph transformation tools.