A variety of graph-based semi-supervised learning (SSL) algorithms and graph construction methods have been proposed in the last few years. Despite their apparent empirical success, the field of SSL lacks a detailed study that empirically evaluates the influence of graph construction on SSL. In this paper we provide such an experimental study. We combine a variety of graph construction methods as well as a variety of graph-based SSL algorithms and empirically compare them on a number of benchmark data sets widely used in the SSL literature. The empirical evaluation proposed in this paper is subdivided into four parts:(1) best case analysis; (2) classifiers' stability evaluation; (3) influence of graph construction; and (4) influence of regularization parameters. The purpose of our experiments is to evaluate the trade-off between classification performance and stability of the SSL algorithms on a variety of graph construction methods and parameter values. The obtained results show that the mutual k-nearest neighbors (mutKNN) graph may be the best choice for adjacency graph construction while the RBF kernel may be the best choice for weighted matrix generation. In addition, mutKNN tends to generate smoother error surfaces than other adjacency graph construction methods. However, mutKNN is unstable for a relatively small value of k. Our results indicate that the classification performance of the graph-based SSL algorithms are heavily influenced by the parameters setting and we found no evident explorable pattern to relay to future practitioners. We discuss the consequences of such instability in research and practice.

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