With very low extra computational cost, the entire solution path can be computed for various learning algorithms like support vector classification (SVC) and support vector regression (SVR). In this paper, we extend this promising approach to semi-supervised learning algorithms. In particular, we consider finding the solution path for the Laplacian support vector machine (LapSVM) which is a semi-supervised classification model based on manifold regularization. One advantage of the this algorithm is that the coefficient path is piecewise linear with respect to the regularization parameter, hence its computational complexity is quadratic in the number of labeled examples.