Machine learning models that can exploit the inherent structure in data have gained prominence. In particular, there is a surge in deep learning solutions for graph-structured data, due to its wide-spread applicability in several fields. Graph attention networks (GAT), a recent addition to the broad class of feature learning models in graphs, utilizes the attention mechanism to efficiently learn continuous vector representations for semi-supervised learning problems. In this paper, we perform a detailed analysis of GAT models, and present interesting insights into their behavior. In particular, we show that the models are vulnerable to heterogeneous rogue nodes and hence propose novel regularization strategies to improve the robustness of GAT models. Using benchmark datasets, we demonstrate performance improvements on semi-supervised learning, using the proposed robust variant of GAT.