Graph-based semi-supervised learning (SSL) methods usually consist of two stages: in the first stage, a graph is constructed from the set of input instances; and in the second stage, the available label information along with the constructed graph is used to assign labels to the unlabeled instances. Most of the previously proposed graph construction methods are unsupervised in nature, as they ignore the label information already present in the SSL setting in which they operate. In this paper, we explore how available labeled instances can be used to construct a better graph which is tailored to the current classification task. To achieve this goal, we evaluate effectiveness of various supervised metric learning algorithms during graph construction. Additionally, we propose a new metric learning framework: Inference Driven Metric Learning (IDML), which extends existing supervised metric learning algorithms to exploit widely available unlabeled data during the metric learning step itself. We provide extensive empirical evidence demonstrating that inference over graph constructed using IDML learned metric can lead to significant reduction in classification error, compared to inference over graphs constructed using existing techniques. Finally, we demonstrate how active learning can be successfully incorporated within the the IDML framework to reduce the amount of supervision necessary during graph construction.