Differential privacy (DP) has been widely adopted to protect sensitive information in graph analytics. While edge-DP, which protects privacy at the edge level, has been extensively studied, node-DP, offering stronger protection for entire nodes and their incident edges, remains largely underexplored due to its technical challenges. A natural way to bridge this gap is to develop a general framework for reducing node-DP graph analytical tasks to edge-DP ones, enabling the reuse of existing edge-DP mechanisms. A straightforward solution based on group privacy divides the privacy budget by a given degree upper bound, but this leads to poor utility when the bound is set conservatively large to accommodate worst-case inputs. To address this, we propose node-to-edge (N2E), a general framework that reduces any node-DP graph analytical task to an edge-DP one, with the error dependency on the graph's true maximum degree. N2E introduces two novel techniques: a distance-preserving clipping mechanism that bounds edge distance between neighboring graphs after clipping, and the first node-DP mechanism for maximum degree approximation, enabling tight, privacy-preserving clipping thresholds. By instantiating N2E with existing edge-DP mechanisms, we obtain the first node-DP solutions for tasks such as maximum degree estimation. For edge counting, our method theoretically matches the error of the state-of-the-art, which is provably optimal, and significantly outperforms existing approaches for degree distribution estimation. Experimental results demonstrate that our framework achieves up to a 2.5x reduction in error for edge counting and up to an 80x reduction for degree distribution estimation.