## 5 Study on the Evolution Network Model of the Landslide Disaster Chain
### Vulnerability Analysis of Connected Edges of the Landslide Disaster Chain Network Model
Among the five parameters, four parameters, including the edge intermediate number, connectivity, average path length, and normalized vulnerability, are selected as a line graph, and the results are shown in Figure 15.  
Based on the findings presented in Table 3 and Figure 15, the following observations were made:  
(1) The connecting edges _R1_, _R3_, and _R5_ exhibit significant edge betweenness values, measuring 80, 55, and 51, respectively. This suggests that these three edges have a substantial impact on the landslide disaster chain network. Conversely, connected edges like _R42_, _R43_, and _R48_ have an edge betweenness of 1, indicating t their limited influence on the overall network. (2) The network's connectivity remains high (0.97) when either R2 or R20 is removed, while the removal of other edges maintains a connectivity of 1. This indicates that the  
Figure 15: Parameters at the connecting edge of the landslide disaster chain evolution network. (**a**) Edge betweenness. (**b**) Connectivity. (**c**) Average path length. (**d**) Normalized vulnerability. presence of the remaining 75 edges strengthens the resilience of the disaster chain network. The hazard associated with _R2_ and _R20_ in the evolution of the landslide disaster chain network exceeds that of the other 75 connecting edges. These two edges form isolated chain structures with no other derived connecting edges. (3) When the connecting edge _R39_, _R38_, or _R37_ are removed, the average path length of the network increases to 4.13, 4.07, and 3.67, respectively. This suggests that cutting off these three edges can effectively slow down the chain reaction caused by disaster events, reduce the likelihood of subsequent disaster, and provide additional time for rescue and disaster mitigation efforts. Conversely, removing _R6_, _R7_, _R8_, or _R9_ result in the smallest average path length (1.80), indicating that the presence of these four edges has minimal impact on the landslide disaster chain. (4) The edge _R1_ is identified as the most vulnerable, followed by _R3_, _R32_, _R39_, _R38_, _R5_, _R15_, _R16_, and _R21_, which also exhibit significant vulnerability. In contrast, _R42_ and _R43_ are considered the least vulnerable edges. Notably, _R1_, _R3_, _R5_, _R15_, _R16_, _R21_, and _R32_ can form a small disaster chain with centralized evolution (Figure 16). Consequently, this small disaster chain represents a vulnerable link within the landslide disaster chain network. It is important to note that the edges with high vulnerability can be categorized into two groups. The first group comprises edges concentrated at the beginning of the disaster chain, such as _R1_ and _R3_. The second group consists of edges concentrated at the incoming edges connected to the central nodes of the disaster chain, exemplified by _R32_, _R39_, and _R38_. These edges share the common characteristic of being associated with numerous nodes, and disrupting these edges can significantly impede the entire disaster chain network, thereby delaying or preventing the occurrence of multiple disaster nodes within the network. In light of the vulnerable links within the western landslide disaster chain evolution network, timely disaster prevention actions can significantly reduce the overall risk associated with this network. (1) High-precision remote sensing technology offers the potential to monitor mountain slope deformations before a landslide disaster occurs (V1). This proactive approach allows for early risk identification, in conjunction with expert evaluations, enabling the implementation of necessary technical measures to mitigate the risk. (2) In the aftermath of a landslide catastrophe (V1), strategically placing barriers in high-risk and critical sections can intercept the downhill movement of landslide debris, reducing the subsequent destructive force of both the landslide (V1) and debris flow (V2). Figure 16: Vulnerable links in the landslide disaster chain evolution network.