## 2 Related Works  
With individual privacy on MWNs attracting more and more attention, various techniques have been proposed to provide privacy preservation. In this section, we will focus on methods that include two categories: graph modification and differential privacy.  
In graph modification, there are three important graph modification methods: edge and node modification methods, generalization or clustering methods, and uncertain graph methods. In edge and node modification methods, to improve data utility, [PERSON]. [7] proposed two algorithms to preserve the original graph while keeping the spectral properties of the graph unchanged as much as possible. In [22], [PERSON] designed a method to protect the most important edges, which obtained a better trade-off between privacy preservation and data utility. In generalization methods that focus on how to generate so-called super-nodes and super-edges, [PERSON]. [23] developed a clustering perturbation algorithm that adopted some perturbations to maintain the whole structure of the social net work and reduce privacy leakages. In uncertain graph methods, [PERSON] in [24] designed a (k, )-obfuscation method based on injecting uncertainty to get an uncertain graph, which was similar to the original graph. To prevent link attacks based on background knowledge, [PERSON] developed an uncertain graph method based on edge-differential privacy, which also had better data utility in [25].  
In addition, k-anonymity [5] had been widely used to generate anonymous graphs to preserve graph data. Considering the number of mutual friends (NMF) between two users, [26] developed a k-anonymity method that made use of the mutual friend sequence to ensure the existence of at least k elements holding the same value for better data utility. In [27], the new (k, l)-degree anonymity algorithm was devised to modify the original networks based on a sequence of edge editing operations. In this algorithm, a location entropy metric was considered to select the important edges so it could achieve minimum edge modification to increase data utility. Meanwhile, to resist insider attacks in collaborative social networks, [28] developed a k-anonymity method based on the clustering, in which a scalable non-deterministic clustering was utilized to prevent the structure attacks.  
In differential privacy methods, many methods based on differential privacy have been presented for graph data since C. [PERSON] came up with differential privacy, which was classified into two kinds: preserving specific sensitive statistics of graphs and generating differential private graphs. For publishing higher order network statistics, i.e., joint degree distribution, [PERSON] [29] designed a general framework for releasing dK-distributions under node differential privacy, in which sensitivity was regulated by a graph projection algorithm, which transformed graphs into bounded graphs. To accurately estimate subgraph counts, [30] proposed a novel multi-phase framework under DDP (decentralized differential privacy), which was able to control the minimum local noise scale to preserve the sub-graph counts. Furthermore, some statistical data in graph data, such as triangle counts, centrality and shortest paths were preserved by differential privacy before they were released [31; 32]. Apart from preserving the statistical data, differential privacy is also applied to generate a synthetic graph. In [33], [PERSON] developed an algorithm to attain a graphical degree partition of a graph preserved by differential privacy, which could also be used to construct synthetic graphs. Ref. [34] proposed an LDPGen, which could generate a synthetic graph after structurally similar users were clustered together according to optimal parameters.