## 6 Case Study
### Structural Robustness Analysis  
Based on the network model construction method described in Section 4.1, Figure 5 depicts the initial cloud manufacturing resource network. Matlab-2020a software was implemented  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Resource**} & \multirow{2}{*}{** \begin{tabular}{c} **Alternative** \\ **Resource** \\ \end{tabular}  } & \multirow{2}{*}{**Re-Source**} & \multirow{2}{*}{** \begin{tabular}{c} **Alternative** \\ **Resource** \\ \end{tabular}  } & \multirow{2}{*}{**Re-Source**} & \multirow{2}{*}{**\ \begin{tabular}{c} **Resource** \\ **Resource** \\ \end{tabular}  } & \multirow{2}{*}{**Re-Source**} & \multirow{2}{*}{** \begin{tabular}{c} **Alternative** \\ **Resource** \\ \end{tabular}  } \\ \hline r1 & r2 & r2 & r1 & r3 & r4 & r4 & r3 \\ r5 & r6 & r6 & r5 & r7 & r8 & r8 & r7 \\ r9 & r10 & r10 & r9 & r11 & r12 & r12 & r11 \\ r13 & r16 & r14 & r15 & r15 & r  
2.1 Structural Robustness Comparison of Three Substitution Strategies under Initial Node Degree Loss (ID) Failure Mode  
As shown in Figure 7, (1) in the ID failure mode, the maximum connectivity subgraphs under the no-substitution strategy (\"common\") and the three resource substitution strategies (\"internal\", \"external\", and \"inter&exter\") all show a decreasing trend as the number of node failures increases. This indicates that from the complex network perspective, the structural robustness of the CMS gradually decreases. (2) The curves of the three resource substitution strategies are all located above the curve of the no-substitution strategy (i.e., their maximum connectivity subgraph values are larger than the no-substitution strategy's value). This indicates that all three resource substitution strategies can improve the structural robustness of the CMS in the face of initial node degree failure. (3) The \"internal\" curve is only slightly higher than the \"common\" curve, and when the number of node attacks is high, the maximum connected subgraph values of these two strategies decrease to 0, at which point the CMN has completely collapsed. In contrast, the \"external\" and \"inter&exter\" curves are significantly higher than the \"common\" curve, and even when the number of node attacks is high, the connected subgraph values still maintain a high level. This indicates that the external replacement strategy and the internal-external integrated replacement strategy both offer more significant robustness enhancement than the internal replacement strategy under the ID failure mode. 2.2 Structural Robustness Comparison of Three Substitution Strategies under Initial Node Betweenness Loss (IB) Failure Mode  
As shown in Figure 8, (1) in the IB failure mode, the maximum connectivity subgraphs under the no-substitution strategy (\"common\") and the three resource substitution strategies (\"internal\", \"external\", and \"inter&exter\") all show a decreasing trend as the number of node failures increases. This indicates that from the complex network perspective, the structural robustness of the CMS gradually decreases. (2) The curves of the three resource substitution strategies are all located above the curve of the no-substitution strategy (i.e., their maximum connectivity subgraph values are larger than the no-substitution strategy's value). This indicates that all three resource substitution strategies can improve the structural robustness of the CMS in the face of initial node betweenness failure. (3) The \"internal\" curve is only slightly higher than the \"common\" curve, and when the number of node attacks is high, the maximum connected subgraph values of these two strategies decrease to 0, at which point the CMN has completely collapsed. In contrast, the \"external\" and \"inter&exter\" curves are significantly higher than the \"common\" curve, and even when the number of node attacks is high, the connected subgraph values still maintain a high level. This indicates that the external replacement strategy and the internal-external  
Figure 7: Variation of S under ID failure mode.