Applying density functional theory we studied magnetism in partially hydrogenated graphene. We demonstrated that the difference in the number of H atoms adsorbed on two graphene sublattices eta can be used as a parameter to predict stability of hydrogen structures on graphene. All favorable structures with even number of H atoms are non-magnetic, with eta equal to zero. Favorable structures with odd number of H adsorbates have eta equal to one, giving rise to a total magnetic moment of 1 mu(B). Structures with higher eta, including recently proposed graphone, are thermodynamically unfavorable and kinetically unstable at room temperature. (C) 2012 Elsevier B. V. All rights reserved.