## 4 The Proposed Method
### DGNDP (Synthetic Directed Graph Based on Node Differential Privacy) Algorithm
#### 4.2.3. GGM (Generating Synthetic Graph Based on Graph Modification)
In particular, the exponent mechanism is adopted to truncate degree sequences, which can ensure that the minimum noise is added to the degree sequences. Moreover, the ranking micro-aggregation effectively reduces the noise added to the degree sequences. According to the noised degree sequences, the relationship between two nodes is utilized to modify the edges of nodes, which can retain the original graph structure. Moreover, the theoretical analysis and the performance of experiments show that the DGNDP method not only satisfies \(\epsilon\)-differential privacy but also retains data utility. In this paper, we only focus on the simple static directed graph without considering node attributes. However, node attributes play an important role in the directed graphs. Thus, in the future, we will concentrate on the application of node differential privacy in complex attribute graphs. In addition, there is still a demand to achieve privacy preservation for dynamic directed graphs. Conceptualization, J.Y. and Y.Z. ; methodology, J.Y. ; software, J.Y. ; validation, J.Y., Y.Z. and L.L. ; formal analysis, J.Y. ; investigation, J.Y. ; resources, J.Y. ; data curation, J.Y. ; writing--original draft preparation, J.Y. ; writing--review and editing, Y.Z. ; visualization, J.Y. ; supervision, Y.Z. ; project administration, L.L. ; funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (62001273, 61962033) the Fundamental Research Funds for the Central Universities (No. 2019 CBLY004 and No. GK201903091), the Scientific and Technological Project of Shangluo (No. 2021-C-0004) and Shangluo Universities Key Disciplines Project, Discipline name: Mathematic. The authors declare no conflict of interest. ## References

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