Abstract: The spine graph construction is an explicit geometric construction that can be used to show moduli spaces of hyperbolic surfaces with boundary are homeomorphic to certain moduli spaces of ‘metric ribbon graphs’. In this talk, I will explain why these homeomorphisms roughly preserve the geometry of these moduli spaces, in particular with respect to the Weil-Petersson and Kontsevich volume forms. Furthermore, I will explain how this result can be used to obtain a convergence-in-mean result on critical exponent random variables.