In this thesis we investigate the effect of disorder in Graphene and nano-meter size Graphene samples. We start by introducing a discrimination parameter (DP) to discriminate localized versus extended states. Then we introduce a numerical method based on the expansion in terms of a complete set of polynomials which is suitable for evaluating of DP and many other spectral functions and improve it to the case of Graphene. Our finding predicts presence of a mobility edge in strongly disordered Graphene.