  We discuss the discrimination of the 125 GeV spin-parity 0^+ Higgs-like boson
observed at the LHC, decaying into two photons, H\to\gamma\gamma, 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 strong discrimination between the
possibilities of spin-0 and spin-2 with graviton-like couplings, depending on
the fraction of q\bar{q} production of the spin-2 signal, reaching a
{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.
