The study of translation surfaces gave birth to a very rich theory, with a large array of powerful results. The study of a given surface is however usually difficult. We concentrate on studying saddle connections (geodesics between singularities), well studied objects that are the interesting close curves inside of a translation surface. We can apply the known concept of curve complex to translation surfaces, defining saddle connection graphs with similar properties: they are invariants for a certain action on translation surfaces and give information on the geometry of the initial surface. Following the interesting properties of this construction on the torus, we investigate some properties of the saddle connection graph of the L shaped surface of ratio φ, better known as the golden L.