PageRank for Semi-Supervised Learning has shown to leverage data structures and limited tagged examples to yield meaningful classification. Despite successes, classification performance can still be improved, particularly in cases of fuzzy graphs or unbalanced labeled data. To address such limitations, a novel approach based on powers of the Laplacian matrix $L^γ$ ($γ> 0$), referred to as $L^γ$-PageRank, is proposed. Its theoretical study shows that it operates on signed graphs, where nodes belonging to one same class are more likely to share positive edges while nodes from different classes are more likely to be connected with negative edges. It is shown that by selecting an optimal $γ$, classification performance can be significantly enhanced. A procedure for the automated estimation of the optimal $γ$, from a unique observation of data, is devised and assessed. Experiments on several datasets demonstrate the effectiveness of both $L^γ$-PageRank classification and the optimal $γ$ estimation.