A key recent advance in face recognition which models a test face image as a sparse linear combination of training face images has demonstrated robustness against a variety of distortions, albeit under the restrictive assumption of perfect image registration. To overcome this misalignment problem, we propose a graphical learning framework for robust automatic face recognition, utilizing sparse signal representations from face images as features for classification. Our approach combines two key ideas from recent work in: (i) locally adaptive block-based sparsity for face recognition, and (ii) discriminative learning of graphical models. In particular, we learn discriminative graphs on sparse representations obtained from distinct local slices of a face. The graphical models are learnt in a manner such that conditional correlations between these sparse features are first discovered (in the training phase), and subsequently exploited to bring about significant improvements in recognition rates. Experimental results show that the complementary merits of existing sparsity-based face recognition techniques - which use class specific reconstruction error as a recognition statistic - in comparison with our proposed approach can further be mined into building a powerful meta-classifier for face recognition.