[en] We built graphene nanoflakes doped or not with C atoms in the sp³ hybridization or with Si atoms. These nanoflakes are isolated, i.e. are not connected to any object (substrate or junction). We used a modified tight binding method to compute the π and σ density of states. The nanoflakes are semiconducting (due to the armchair geometry of their boundaries) when they are pure but they become conducting when doped because doping removes the degeneracy of the density of states levels. Moreover, we showed that the π Fermi level and the Fermi level of both π and σ electrons are not superimposed for small isolated nanoflakes.