## 2 Greedy Strategy Based on Edge Importance  
The EG algorithm uses greedy strategy that requires an importance measure for the edges in a network before each use. It works by adding known important nodes to a set \(C\) that includes all their neighbors, after which one can assign an importance score to the connected edges of the known important nodes based on the topological information of the network. The importance score can be calculated as follows:  
\[SV=\frac{k_{j}}{k_{i}}\cdot\frac{1}{d^{2}}+\frac{1}{cn+1} \tag{1}\]  
where \((k_{j}/k_{i})\cdot(1/d^{2})\) is an important component called \(NP\) value, which measures the importance of a certain node; \(k_{i}\) is the degree of known important node \(i\); \(k_{j}\) is the degree of known important neighbor node \(j\); \(d\) is the shortest distance between node \(j\) and the set of known important nodes; and \(cn\) is the number of common neighbors of node \(j\) and known important nodes. The core idea of Equation (1) is actually very straightforward: the larger the \(k_{j}\) is, the greater the importance of node \(j\). On the other hand, since \(d\) is the shortest distance between node \(j\) and the set of known important nodes, the larger the \(d\) is, the smaller the value of \(1/d^{2}\). A small \(k_{j}\) or a large \(d\) results in a smaller \(NP\), and thus a lower importance score for node \(j\). In other words, nodes with low degree and large distance from known important nodes tend to have lower importance, and vice versa. In particular, there will be cases where two nodes have the same \(NP\) value. In order to solve this problem, a bias value \(1/(cn+1)\) is added to Equation (1) to distinguish their importance. Once the importance score is obtained, the greedy strategy is used to find the node whose edge has the largest score from an edge set that corresponds to known important nodes. The found node will then be added to set \(C\). The edge scores corresponding to each node in set \(C\) will be again calculated, and the node will be found by using the same strategy stated previously. This process is repeated until all nodes are added. The order in which nodes are added to set \(C\) is exactly the order of their importance. The pseudo-code for the EG algorithm, also known as Algorithm 1, is as follows:  
```
0: Input Network \(G=(V,E)\), the set of known important nodes \(R\);  Initialization \(C=R\); \(S=0\);
1: While the number of elements in \(C\) is less than \(|V|\)do:
2:for\(i\) in \(C\)do:
3:for\(j\) in \(i\) neighbors do:
4:\(SV(i,j)=k\_{j}/k\_{i}\cdot 1/d2+1/(cn+1)\);
5:endfor
6:\(t=\{j|\text{max}(SV)\}\);
7: Place the node \(t\) into set \(C\);
8:endfor
9:endwhile
10:return\(C\)
```  
**Algorithm 1** EG Algorithm  
The EG algorithm is divided into three parts, which are as follows: computation of the shortest path of a single source; computation of the node importance score; and selection of the greedy policy. The EG algorithm chooses to compute the neighboring nodes of known important nodes. Lines 1-2 of the algorithm are the traversal of the set \(C\), and the nodes in it are computed and analyzed. Lines 3-5 of the algorithm calculate the node importance score by first selecting a node \(i\) from among the set of known important nodes, then traversing its neighbor nodes and calculating the importance score of each neighboring node. Lines 6-8 of the algorithm apply a greedy strategy to select nodes, and the node with the highest \(SV\) is added to set \(C\). The above process is repeated until all nodes are added to set \(C\). It can be found that the time complexity of the EG algorithm depends mainly on the calculation of the shortest path of a single source and the importance score. It is easy to see that the calculation of the node importance score is a cumulative process, and depends on the degree of the important nodes.