Graph clustering is a fundamental task in network analysis, with applications ranging from community detection to protein complex identification. While Graph Neural Networks (GNNs) have shown promising results in this domain, they often struggle to balance local structure preservation with global cluster separation. We present a novel information-theoretic framework that enhances graph clustering through differentiable Rényi entropy optimization. Our approach introduces a computationally efficient masked entropy loss that encourages informative node representations while respecting graph topology. By integrating this framework with state-of-the-art GNN architectures, we achieve significant improvements in clustering quality across multiple benchmark datasets.