Clustering plays a pivotal role in exploratory data analysis, especially in scenarios where prior knowledge about a subset of samples is available, prompting a rapid development of Semi-supervised clustering approaches. In this work, we introduce a novel method for seamlessly integrating prior knowledge into the widely recognized Normalized Cut Clustering (NCC) algorithm, thereby offering a natural extension within the realm of semi-supervised clustering. Similarly to NCC, the solution of the proposed method is spectral-based in the form of an inhomogeneous eigenvalue problem. Also, we show that the proposed method can be seen as a generalization of NCC, enhancing its applicability in scenarios where prior information is available. In addition, we design an adequate and comprehensive experimental setup. This setup not only tests the competitiveness of our approach but also showcases its superiority in terms of performance metrics.