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The use of unlabeled data has lead to an improvement in classification accuracy for a variety of classification problems via co-training approaches. In the co-training approach, the data has to be available in a dual view representation or two distinct classifiers are required. In this paper, a unified energy equation for classification combining labeled data and unlabeled data is introduced. This classification formulation is posed as a constrained minimum cut problem integrating labeling information on labeled data and cluster similarity information on unlabeled data for joint estimation. A novel constrained randomized contraction algorithm is proposed for finding the solution to the constrained minimum cuts problem. Experimental results on standard datasets and synthetic datasets are presented.