# A Differentiated Anonymity Algorithm for Social Network Privacy Preservation
## 3 The Differentiated Attribute-Preserving Model
### The Differentiated Attribute-Preserving Algorithm
#### 3.2.1 Basic Idea  
Given a graph G(V,E,A,S), the attacker's background knowledge F, which is the degree of the target node and the privacy requirement \(k\), \(l\), we perform node(Vi\(\in\)V) segmentation operations one at a time on G to achieve \(k\)-\(d\)-\(l\)-\(d\) anonymity. To achieve the differentiated anonymity of targeting for decreasing utility loss, our DKDLD-UL algorithm will run the following two main steps:  
Firstly, we define the sensitivity for privacy attribute values with Equation (1), only considering attribute values with S equal to H or M as the privacy, and then put nodes which have privacy attribute values into the privacy-preserving requirements list SV = [Vi].  
Secondly, for targeting node differentiation, we classify the user node set SV into two categories by the key node analysis in social network analysis according to the \"80/20 Rule\" for the convenience in evaluating the experimental algorithm. The details are as follows:  
We choose 20% of the nodes from the set V as key nodes on the basis of the research on four indicators which are commonly used in undirected network node importance analysis and then putthem into the set KV = {Vt}, simultaneously considering other nodes as general nodes GV. The four indicators mentioned above are as follows:  
Degree Centrality  
\[\text{DC}_{\text{i}}=\frac{\text{K}_{\text{i}}}{\text{N}-1} \tag{3}\]  
where Ki is the degree or node Vi and N is number of nodes in set V. However, it has its limits by only considering that the greater the degree of a node, the more important the node.  
Betweeness Centrality (BC)  
\[\text{BC}_{\text{i}}=\sum_{\text{s}\
eq\text{i}\
eq\text{t}}\frac{\text{n}_{ \text{st}}^{\text{i}}}{\text{g}_{\text{st}}} \tag{4}\]  
where \(\text{g}_{\text{st}}\) is the number of the shortest path length between node s and node t and \(\text{n}_{\text{st}}^{\text{i}}\) is the number though node i. The index BC depicts the influence of nodes on the network information flow.  
Closeness Centrality  
\[\text{CC}_{\text{i}}=\frac{1}{\text{d}_{\text{i}}}=\frac{\text{N}}{\sum\limits _{\text{j}=1}^{\text{N}}\text{d}_{\text{ij}}} \tag{5}\]  
where \(\text{d}_{\text{ij}}\) is the distance between node V\({}_{\text{i}}\) and node V\({}_{\text{j}}\). In experiments, the parameter shows an effective description of a node's topological importance.  
Eigenvector Centrality  
\[\text{x}_{\text{i}}=\text{c}\sum\limits_{\text{j}=1}^{\text{N}}\text{a}_{ \text{ij}}\text{x}_{\text{j}} \tag{6}\]  
where c is a constant and A = (a\({}_{\text{ij}}\)) is the adjacency matrix. This shows not only a high number of neighbor nodes but is also an effective description of a node's topological importance.  
Above all, in the simulation experiments, we use the last three indicators to mine the central nodes and we may change the measure index of different social networks.  
Thirdly, for the two sets of nodes in the network, we use different anonymizing operations separately from node division operations for key nodes in set KV, and with privacy attribute value generalization operations for other nodes in set GV.