The present work deals with data-adaptive active sampling of graph nodes representing training data for binary classification. The graph may be given or constructed using similarity measures among nodal features. Leveraging the graph for classification builds on the premise that labels over neighboring nodes are correlated according to a categorical Markov random field (MRF). This model is further relaxed to a Gaussian (G)MRF with labels taking continuous values, an approximation that not only mitigates the combinatorial complexity of the categorical model, but also offers optimal unbiased soft predictors of the unlabeled nodes. The proposed sampling strategy is based on querying the node whose label disclosure is expected to inflict the largest expected mean-square deviation on the GMRF, a strategy which subsumes the existing variance-minimization-based sampling method. A simple yet effective heuristic is also introduced for increasing the exploration capabilities, and reducing bias of the resultant estimator, by taking into account the confidence on the model label predictions. The novel sampling strategy is based on quantities that are readily available without the need for model retraining, rendering it scalable to large graphs. Numerical tests using synthetic and real data demonstrate that the proposed methods achieve accuracy that is comparable or superior to the state-of-the-art even at reduced runtime.