Using traditional k-anonymization techniques to achieve privacy protection in social networks is faced with problems such as single clustering criterion and under-utilization of data and information in the graph. To solve this problem, this study proposes an anonymization technique measuring the similarity of the node 1-neighbor graph based on the Kullback-Leibler divergence (SNKL). The original graph node set is divided according to the similarity of node 1-neighbor graph distribution, and the graph is modified according to the divided classes so that the modified graph satisfies k-anonymity. On this basis, the anonymous release of the graph is implemented. The experimental results show that compared with the HIGA method, the SNKL method reduces the amount of change in the clustering coefficients by 17.3% on average. Moreover, the overlap ratio between the importance nodes of the generated anonymous graph and those of the original graph is maintained at more than 95%. In addition to protecting privacy effectively, the proposed method can significantly reduce the changes brought to the structural information in the original graph.