## 5 Study on the Evolution Network Model of the Landslide Disaster Chain
### Analysis on the Importance of Nodes in the Landslide Disaster Chain Network Model  
(1) Node degree \(J_{i}\)  
In the evolutionary network model of the disaster chain, the node degree consists of both the node entry degree \(J_{ii}\) and the node exit degree \(J_{io}\). The node entry degree represents the count of prior crisis events that can initiate the current catastrophe. A higher r entry degree implies that more disaster elements can trigger the disaster event, increasing the event's likelihood. The node exit degree signifies the number of subsequent disaster events that can be induced by the current disaster event. A higher exit degree results in a wider range of subsequent disasters stemming from the initial catastrophe and more severe disaster consequences [54; 55]. \(J_{i}=\sum_{i=1,i\
eq j}^{N}A_{i-j}\)  
\(A_{i-j}\)--Number of connecting edges between nodes \(V_{i}\) and \(V_{j}\);  
\(N\)--Total number of nodes in the disaster chain network. (2) Node degree centrality \(C_{i}\)  
This indicator represents the ratio of the actual number of disaster events connected to the current node to the maximum number of possible connections. It reflects the importance and influence of the current disaster events within the disaster chain network. \(C_{i}=\dfrac{K_{i}}{N-1}\)  
\(K_{i}\)--Number of nodes associated with node \(V_{i}\);  
\(N\)--Total number of nodes in the disaster chain network. (3) Clustering coefficient \(G_{i}\)  
This indicator represents the ratio of the actual number of connections between hazardous events at neighboring nodes of the current hazard \(V_{i}\) to the maximum possible number of connections. It can reflect the tightness of connection between hazards in the hazard chain. \(G_{i}=\dfrac{2 Si}{n(n-1)}\)  
\(S_{i}\)--The actual number of connected edges between \(n\) adjacent nodes of node \(V_{i}\);  
\(n\)--Number of nodes with adjacent edges to node \(V_{i}\). In addition, the disaster chain evolution network clustering coefficient is  
\(G=\dfrac{1}{N}\sum_{i=1}^{N}G{i}\). A higher \(G\) value indicates a better overall concentration of the disaster chain evolution network [56]. The node degree correlation calculations were performed for the landslide disaster chain evolution network model in Figure 10 using Formulas (1)-(4), This yielded the node degree and clustering coefficient for each disaster event, as shown in Figures 13 and 14. According to Figures 13 and 14, the following information can be known:  
(1) In the evolution process of a landslide disaster chain, flood, debris flow, secondary landslide, downstream flood, and other disaster events exhibit a high incidence. This suggests that these disasters have a profound impact on subsequent events and are more likely to trigger subsequent multi-disaster events. High casualty rates, economic losses, and animal husbandry injuries indicate that other disasters may also lead to varying degrees of casualties and economic losses. Examining the network's overall connectivity, dam break, road damage, and damage to power facilities, among other intermediate disaster events, have node degrees exceeding 5. This implies that these disaster nodes wield significant influence in the disaster chain network and are closely related to other disaster events. They represent important factors contributing to economic losses in the landslide disaster chain. (2) Within the evolutionary network of landslide hazard chains, 15 disaster events have clustering coefficients greater than 0, representing 48.4% of the total number of hazardous events. Among these, plague or infectious disease, casualties, secondary landslides, and damage to power facilities have higher clustering coefficients, indicating closer linkages compared to others. However, none of them are clustered to a high degree. The clustering coefficient \(G=0.061\) was calculated for this hazard chain network diagram, suggesting that numerous factors contribute to eventual economic losses and human casualties throughout the landslide disaster chain risk evolution process.