The article introduces a new method for applying Quantum Clustering to graph structures. Quantum Clustering (QC) is a novel density-based unsupervised learning method that determines cluster centers by constructing a potential function. In this method, we use the Graph Gradient Descent algorithm to find the centers of clusters. GPU parallelization is utilized for computing potential values. We also conducted experiments on five widely used datasets and evaluated using four indicators. The results show superior performance of the method. Finally, we discuss the influence of $σ$ on the experimental results.