This paper highlights the molecular essence of graphene and presents its hydrogenation from the viewpoint of the odd-electron molecular theory. This chemical transformation was performed computationally, using a particular algorithm, through the stepwise addition of either hydrogen molecules or hydrogen atoms to a pristine graphene molecule. The graphene was considered to be a membrane, such that either both sides or just one side of the membrane was accessible to adsorbate, and the atoms on the perimeter of the membrane were either fixed (fixed membrane) or free to move (free-standing membrane). The algorithm explored the spatial distribution of the number of effectively unpaired electrons NDA over the carbon skeleton of the molecule. The highest ranked NDA values were considered to indicate the target atoms at each reaction step. The dependence of the hydrogenation itself and the final graphene hydrides on external factors such as whether the membrane was fixed, if both sides or only one side of the membrane were accessible to hydrogen, and whether the hydrogen was in the molecular or atomic state. Complete hydrogenation followed by the formation of a regular chairlike graphane structure (CH)n was only found to be possible for a fixed pristine graphene membrane for which the basal plane is accessible to hydrogen atoms from both sides. © Springer-Verlag 2012.