Label Propagation is a semi-supervised learning algorithm typically applied to partially labeled graph data sets for classifying unlabeled nodes. Similar to the Personalized PageRank algorithm, Label Propagation is in essence a random walk on a graph, resting on the assumption that similar nodes are more likely to form edges. Graph based models and analysis inform companies about their customers and help make recommendations for targeted ad placement when databases are sparse. We generalize the concept of label propagation to constrain the random walk to regions of the search space where the true solution may lie based on prior knowledge. Specifically, we reformulate the label propagation algorithm as a minimum energy control problem that embraces traditional label propagation as a special case. We apply the formulation to (i) benchmark data sets, and (ii) the Yelp challenge data set. Results indicate the approach is comparable to competing methods for the benchmark data. For the Yelp data, our experiments show a promising 20%-50% improvement over the baseline for select business features.