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Graph based semi-supervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method and its effect on performance. This article provides an empirical study of leading semi-supervised methods under a wide range of graph construction algorithms. These SSL inference algorithms include the Local and Global Consistency (LGC) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular k-nearest neighbors method (kNN) and the b-matching …