We discuss the discrimination of the 125 GeV spin-parity 0 + Higgs-like boson observed at the LHC, decaying into two photons, H → γ γ , against the hypothesis of a minimally coupled J P = 2 + narrow diphoton resonance with the same mass and giving the same total number of signal events under the peak. We apply, as the basic observable of the analysis, the center-edge asymmetry A CE of the cosine of the polar angle of the produced photons in the diphoton rest frame to distinguish between the tested spin hypotheses. We show that the center-edge asymmetry A CE should provide a strong discrimination between the possibilities of spin-0 and spin-2 with graviton-like couplings, depending on the fraction of qq production of the spin-2 signal, reaching CL s < 10 −6 for f qq = 0. Indeed, the A CE has the potential to do better than existing analyses for f qq < 0.4.