# Understanding Safety Performance of Prefabricated Construction Based on Complex Network Theory
## 4 Result
### Vital Node Identification  
Based on the conclusion elicited from topological analysis, PCSRN manifests the small-world and scale-free characteristics inherently, and only the key nodes can be controlled to disrupt the transmission cascade of safety risks in the network. With the four indicators introduced above, a node influence-based analysis was performed to distinguish the vital nodes worthy of special attention. Table 8 exhibits the top fifteen ranking in the eigenvector centrality, degree difference, HITS, and k-shell decomposition. Nodes ranked in the top three in each of these four indicator results are highlighted in bold. R22 (Inadequate safety education and training), R3 (Design variations), and R1 (Lack of safety considerations in design) score high on eigenvector centrality since they have positive ties with most central (popular) actors in the network. In terms of the metric of the degree difference, R21 (Poor organizational communication), R22 (Inadequate safety education and training), and R1 (Lack of safety considerations in design) are regarded as factors with a prominent net influence level. Three safety risks ranked in accordance with authority scores of HITS are confirmed to be R20 (Unsecured equipment/ tool/ object), R16 (Quality defects of prefabricated components), and R18 (Insufficient connection strength of prefabricated components). According to hub scores of HITS, R1 (Lack of safety considerations in design), R3 (Design variations), and R2 (Error in design) are the most efficient propagators controlling over the connectivity of network structures. With regard to k-shell decomposition indicator, there are 14 triangular nodes with a k-shell score of 4 as presented in Figure 6. The result is relatively coarse since the nodes with the same k-shell score cannot be compared horizontally. Therefore, k-shell decomposition method is applied as an auxiliary method to identify key nodes in this paper. What is obvious from the outcomes is that the top three safety risks in each of the indicator analysis results are partially overlapped and consistent. In fact, almost all the top three nodes of eigenvector centrality, degree difference and HITS also own the maximum \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**The Random Network**} & \multicolumn{8}{c}{**No.**} \\ \cline{2-11}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Clustering coefficient & 2.033 & 2.127 & 2.266 & 2.349 & 2.233 & 2.212 & 2.195 & 2.321 & 2.349 & 2.478 \\ Average path length & 0.065 & 0.041 & 0.071 & 0.053 & 0.07 & 0.069 & 0.076 & 0.072 & 0.053 & 0.046 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The average path length and clustering coefficient of 10 random networks. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Rank**} & \multirow{2}{*}{**Risk ID**} & \multicolumn{2}{c}{**Eigenvector**} & \multirow{2}{*}{**Risk ID**} & \multicolumn{2}{c}{**Degree**} & \multirow{2}{*}{**Risk ID**} & \multicolumn{2}{c}{**HITS**} & \multirow{2}{*}{**Risk ID**} & \multicolumn{2}{c}{**HITS**} & \multirow{2}{*}{**Risk ID**} & \multicolumn{2}{c}{**k-Shell Decomposition**} \\  & & **Centrality** & & & & & & & & & \\ \hline
1 & R22 & 0.288456 & R21 & 5 & R20 & 0.489881 & R1 & 0.509800 & R1 & 4 \\
2 & R3 & 0.276495 & R22 & 5 & R16 & 0.409649 & R3 & 0.367013 & R2 & 4 \\
3 & R1 & 0.276237 & R1 & 5 & R18 & 0.33  
K-shell value of 4, which characterizes them as the most influential nodes in PCSRN. Eight risks on aggregate are identified as the critical construction safety risks of prefabricated building projects, including R22 (Inadequate safety education and training), R21 (Poor organizational communication), R1 (Lack of safety considerations in design), R3 (Design variations), R2 (Error in design), R20 (Unsecured equipment/tool/object), R16 (Quality defects of prefabricated components), and R18 (Insufficient connection strength of prefabricated component).