## 3 Construction of the Basic Network
### Calculation Method for Assessing Vulnerability and Demand Coverage of Road Sections  
The reference indicators utilized for the calculation of road section vulnerability are presented in the Table 2.  
In the table, \(\mathrm{E(G)}\) denotes the efficiency of the original network, while \(\mathrm{E(G-r)}\) signifies the efficiency of the network following the removal of a specific road section r. Additionally, \(\mathrm{n^{\prime}}\) represents the number of nodes in the largest connected sub-graph and n indicates the total number of nodes in the original network. The variable \(\mathrm{\sigma_{st}}\) refers to the number of shortest paths between nodes s and t, whereas \(\mathrm{\sigma_{st}(r)}\) represents the number of shortest paths that traverse the road section r. Furthermore, \(\mathrm{D_{st}}\) denotes the logistics demand between nodes s and t. The change rate of network efficiency and the relative size of the largest connected subgraph are considered as static indicators, whereas the significance of road sections is classified as a dynamic indicator, necessitating calculation based on the actual conditions of the road network. In conclusion, the implementation of the vulnerability assessment algorithm is illustrated in Figure 3 and pseudo-code.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator Name** & **Calculation Formula** & **Physical Interpretation** \\ \hline Network Efficiency Change Rate & \(\mathrm{E_{v}(i)}=\frac{\mathrm{E(G)-E(G-r)}}{\mathrm{E(G)}}\) & This statement indicates the extent of the decline in the overall connectivity performance of the network. \\ \hline Relative Size of the Largest Connected Subgraph & \(\mathrm{S(G-i)}=\frac{\mathrm{n^{\prime}}}{\mathrm{n}}\) & This assessment analyzes the current state of network segmentation and evaluates the integrity of the overall structure. \\ \hline Section Importance & \(\mathrm{I_{r}}=\sum\limits_{\mathrm{s,t\in V}}\frac{\mathrm{\sigma_{st}(r)}}{ \mathrm{\sigma_{st}}}\mathrm{D_{st}}\) & Section on betweenness centrality with consideration of demand weighting \\ \hline \hline \end{tabular}
\end{table}
Table 2: Calculation indicators for assessing vulnerability of road sections.  
The pseudo-code for the execution of the algorithm is presented in Algorithm 2.  
Input: Road network \(\mathrm{G}=(\mathrm{V},\mathrm{E})\)  
Output: Comprehensive vulnerability scores of each road section in the road network \(\mathrm{G}\)  
1. Set the initial network efficiency \(\mathrm{E}(\mathrm{G})\)  
2. For each road section \(\mathrm{r}\)  
2.1 Temporarily remove the road section \(\mathrm{r}\)  
2.2 Calculate the new network efficiency \(\mathrm{E}(\mathrm{G}-\mathrm{r})\)  
2.3 Calculate the change rate of network efficiency \(\mathrm{E}_{\mathrm{v}}(\mathrm{r})\)  
2.4 Calculate the relative size of the largest connected sub-graph \(\mathrm{S}(\mathrm{G}-\mathrm{r})\)  
2.5 Restore the road section \(\mathrm{i}\)  
3. Calculate the comprehensive vulnerability score based on all indicators  
The assessment of demand coverage within the road network is contingent upon the vulnerability of the road network itself. The formula for its calculation is presented as follows:  
\[\mathrm{Coverage}=\frac{\sum_{\mathrm{i}\in\mathrm{C}_{\mathrm{covered}}} \mathrm{D}_{\mathrm{i}}\cdot(1-\mathrm{V}_{\mathrm{r}}(\mathrm{i}))}{\sum_{ \mathrm{i}\in\mathrm{C}_{\mathrm{all}}}\mathrm{D}_{\mathrm{i}}} \tag{26}\]  
Among the elements considered, \(\mathrm{C}_{\mathrm{covered}}\) denotes the set of customers covered by the scheme. Additionally, \(\mathrm{C}_{\mathrm{all}}\) denotes the set of all customers. Furthermore, \(\mathrm{V}_{\mathrm{r}}(\mathrm{i})\) signifies the vulnerability value of the road section where customer \(\mathrm{i}\) is located.