# Understanding Safety Performance of Prefabricated Construction Based on Complex Network Theory
## 3 Methodology
### Network Analysis
#### 3.3.2 Nodes Ranking  
Intuition clearly indicates that not all nodes are equally important for their different roles in structure and function. For the purpose of quantifying the importance of nodes and identifying vital influential nodes, diverse ranking criteria have been coined from different perspectives including global information [88] (such as closeness centrality, betweenness centrality, and eigenvector centrality), local information [89] (such as degree, semi-local, and H-index), random walk [90] (such as PageRank, LeaderRank, and HITS), and position [91] (such as K-shell decomposition, MDD, and INK). Different ranking criteria provide insights into different dimensions of importance. Therefore, taking these four kinds of criteria into consideration, eigenvector centrality, degree difference, HITS, and K-shell decomposition are employed to rank nodes' importance and discover vital nodes in PCSRN.  
Eigenvector Centrality is a more sophisticated view of centrality which evaluates centrality or popularity score of a node while giving consideration to the importance of its neighbors. Nodes with a small number of influential contacts may have higher eigenvector centrality than nodes with a large quantity of mediocre contacts [92]. Mathematically, the eigenvector centrality of a node is the sum of the neighbors' eigenvector centralities divided by \(\lambda\)--the largest eigenvalue of the adjacency matrix of the network [93]. From the perspective of propagation, high eigenvector centrality is helpful for discerning critical nodes with long-term influence.  
The node degree refers to the number of direct connections of a node. Due to the different connection directions of nodes, the degree of nodes in a directed network can be divided into out-degree and in-degree. In some cases, special attention needs to be paid to the distinction between out-degree and in-degree. The concept of degree difference is proposed, which is calculated by subtracting the in-degree from the out-degree of a particular node, to express the net influence level of the node. A high degree difference implies that a node is more likely to influence other nodes in the network than to be affected.  
HITS  
HITS algorithm is a classic web sorting algorithm. As nodes may play different roles in directed networks, it evaluates the influence of each node through mutual correction iteration of two aspects: authority and hub [94]. Hubs and authorities exhibit a reciprocally reinforcing relationship: a high-quality hub points to many authorities, and a high-quality authority is pointed at by many hubs [95]. In a directed network, the authority score of a node is calculated by adding the hub scores of all nodes pointing to the node, and the hub score of a node is summed by the authority scores of all nodes pointing to the node. A high authority score means that the node contains more useful information, and a higher hub score signifies that the node has a more prominent status in information transmission.  
K-shell (also known as K-core) decomposition is a method of coarsely granulating the nodes' spreading influence according to their positions in the network [96]. The location of a node is defined by k-shell decomposition analysis. This process recursively strips the nodes in the network with degrees less than or equal to \(k\) and assigns each node an integer index or coreness, \(k_{s}\), standing for its position according to successive layers (\(k\) shells) in the network. Apparently, a node with a larger coreness indicates that the node is located in a more central position and is possibly more influential in the network.