The high uncertainty of distributed renewable energy, coupled with the complex statistical correlations among photovoltaic (PV) output power profiles across different geographical locations, significantly increases the difficulty of power system operation and planning. Efficient extraction of representative PV power generation scenarios is essential for reducing the computational burden of optimization models and improving decision-making efficiency. To address the challenge, a novel graph clustering model based on shared weight and adaptive fusion is proposed, which effectively captures the correlation among multiple PV power stations and extracts representative scenarios. An alternating optimization algorithm based on the Lagrange multiplier method and eigenvalue decomposition is proposed to obtain the global optimal solution with fast convergence, thereby improving computational efficiency. The highlight of this work is the dual validation through systematic theoretical proofs and multiple dimensional simulation experiments. In terms of theoretical proof, the low sensitivity of the model parameters ensures ease of use in real-world settings, while the proven convergence of the algorithm guarantees computational reliability. In terms of simulation experiments, the proposed clustering model is verified to have collaborative optimization capability, feature identification capability, high cohesion, low coupling, noise resistance, and parameter sensitivity, as well as the convergence of the solution algorithm using actual PV data from Australia. The effectiveness of this work in extracting representative scenarios of the PV output is verified through the probabilistic power flow analysis using the IEEE 69-bus network, significantly enhancing the efficiency and credibility of power system planning studies with high renewable penetration.