  Using density functional theory (DFT), Hartree-Fock, exact diagonalization,
and numerical renormalization group methods we study the electronic structure
of diluted hydrogen atoms chemisorbed on graphene. A comparison between DFT and
Hartree-Fock calculations allows us to identify the main characteristics of the
magnetic structure of the defect. We use this information to formulate an
Anderson-Hubbard model that captures the main physical ingredients of the
system, while still allowing a rigorous treatment of the electronic
correlations. We find that the large hydrogen-carbon hybridization puts the
structure of the defect half-way between the one corresponding to an adatom
weakly coupled to pristine graphene and a carbon vacancy. The impurity's
magnetic moment leaks into the graphene layer where the electronic correlations
on the C atoms play an important role in stabilizing the magnetic solution.
Finally, we discuss the implications for the Kondo effect.
