# Research on Supply Chain Network Resilience: Considering Risk Propagation and Node Type
## 4 Numerical Simulation
### How Scalar Indices Affect SCNR  
We simulated the risk propagation process on SCNs with different scalar indices. Figures 2 and 3 show the resilience changes with different scalar indices at each time step when using resilience metrics \(y\) and \(s\), respectively. The curves in different colors in the figures represent SCNs with different scalar indices, the horizontal coordinate is the time step, and the vertical coordinate is the SCNR at this time step.  
We used resilience metric \(y\) to measure the SCNR at each time step. In Figure 2, the curve drops sharply in the initial phase. When the curve fluctuates less frequently, the risk propagation reaches a steady state. Observing the resilience of SCNs with different scalar indices at the same time step, a larger e implies a larger SCNR. When \(T\) = 20, the system has reached a steady state, at which point we ran another 80 time steps and averaged these \(y\) values to obtain \(Y\). When \(Y\) was used to measure the SCNR, the change in SCNR with different scalar indices is shown in Figure 4. In Figure 4, when \(e\) = 2.0, \(Y\) = 0.0009. When \(e\) = 3.0, \(Y\) = 0.0172. As \(e\) increases, the curve keeps rising and the value of \(Y\) increases. The experimental results under this resilience metric show that the larger the value of an SCN's scalar index network characteristics, the more resilient that SCN is.  
Similarly, we used the resilience metric s to measure the SCNR at each time step. The change in SCNR with different scalar indices is shown in Figure 3. The change pattern of the curve in Figure 3 is similar to that in Figure 2, and we used the same method to obtain \(S\). The SCNR measured by the resilience metrics \(y\) and \(s\) differs by a factor of 10. This indicates that using \(s\) as the resilience metric is relatively coarse, while \(y\) is more delicate.  
Figure 2: The resilience of SCNs at each time step for different scalar indices when using the resilience metric \(y\).  
In Figure 5, when \(e=2.0\), \(S=0.2225\). When \(e=3.0\), \(S=0.3684\). Although the SCNR is minimal when \(e=2.1\), the overall trend of the curve is slowly increasing. When measured by this elasticity metric, \(S\) increases with \(e\). The resilience metrics \(Y\) and \(S\) yield the same conclusion, indicating that \(Y\) is valid. The \(p\)-value method is a common method for statistical tests, where if \(p<0.01\), a significant effect is indicated, and if \(p<0.05\), an effect is indicated [68]. The \(p\)-values calculated under both resilience metrics are much less than 0.01. This indicates that \(e\) has a significant effect on SCNR.  
Finally, the reasons for such experimental results are analyzed. Nodes with large degrees have more influence on risk propagation. The larger \(e\) is in an SCN, the fewer nodes have large degrees, and the more uniform network degree distributions are. Thus, the larger the scalar index, the lower the risk propagation impact and the higher the SCNR.  
Figure 4: The resilience of SCNs for different scalar indices when using the resilience metric \(Y\).  
Figure 3: The resilience of SCNs at each time step for different scalar indices when using the resilience metric \(s\).