Abstract: Graph clustering based on local differential privacy has become a hot research topic in recent years. Most existing solutions are mainly realized through modular aggregation using bit vector technology. The linear relationship between the amount of noise and the vector dimension makes balancing clustering quality and privacy challenges. Aiming at the above problems, a directed graph clustering algorithm, DGC-LDP (directed graph clustering under LDP), is proposed based on edge local differential privacy (Edge-LDP). Concretely, the direct encoding method replaces the bit vector encoding method to reduce the amount of data in privacy processing. Meanwhile, a dynamic perturbation mechanism is designed based on the graph structure to balance privacy and statistical utility by adaptively adding noise. Then, according to the individual information uploaded by the terminal, the collector extracts the similarity information between nodes and designs a node aggregation algorithm based on the silhouette coefficient measurement model to generate clusters. Finally, an iterative mechanism is built between the terminal and the collector, and the collector iteratively optimizes the node aggregation form based on the statistical information fed back by the mechanism to achieve high-quality clustering. Theoretical analysis and experimentation on real-world datasets demonstrate that our proposed algorithm can obtain desirable clustering results while satisfying Edge-LDP.