## 3 Construction of the Basic Network
### Road Network Modeling  
An examination of the vulnerability of regional road networks serves as the foundation for the dynamic collaborative delivery planning presented in this paper. The modeling of road networks is essential for conducting vulnerability analyses. Consequently, the development of the fundamental network is of paramount importance. In order to accurately represent critical information, including the topological structure of urban road networks and the distribution of traffic flow, and to enhance the precision of vulnerability identification, this study employs an original methodology to construct the network topological graph.  
The segments of the road and the intersections within the existing road network are represented as edges and nodes in the corresponding graph. A topological graph of the road network, characterized by a grid-like structure, is developed based on the interconnections among the nodes. The foundational network is constructed with reference to the topological structure of the road network as outlined by [PERSON] and [PERSON], as illustrated in Figure 2. As illustrated in the figure, the gray nodes representing demand points within the road network correspond to the aggregate delivery demands of all users situated in the vicinity of each node. The yellow nodes denote distribution centers tasked with fulfilling deliveries to these demand points. The numeral adjacent to each edge in the diagram denotes its corresponding edge number within the graph. Typically, the quantity of distribution centers is fewer than that of the demand points. Furthermore, in consideration of the delivery distance costs, it is advisable for the distribution centers to be strategically positioned in proximity to the central area of the demand points. Additionally, it is important to note that the locations of the distribution centers also generate demand, thereby categorizing them as demand points in their own right. Table 1 offers additional clarification regarding the node demands and deliveries illustrated in Figure 2. In this context, the demand at each node signifies the aggregate demand from all users associated with that node, while the distribution center denotes the specific distribution center tasked with fulfilling the delivery to the respective demand point.  
In the topological structure of the road network, the delivery network is represented as an undirected weighted graph. The set of nodes comprises road  
Figure 2: Road network topological structure diagram of [PERSON] and [PERSON] [24].  
demand points, distribution centers, and potential take-off and landing locations. The edges of the graph signify the road segments that connect these intersections, with the weight assigned to each edge reflecting the cost or distance associated with traversing that segment. To facilitate calculations, the information pertaining to the road network can be effectively represented using an adjacency matrix [25].  
\[\text{A}=\begin{pmatrix}\text{a}_{11}&\text{a}_{12}&\dots&\text{a}_{1n}\\ \text{a}_{21}&\text{a}_{22}&\dots&\text{a}_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ \text{a}_{n1}&\text{a}_{n2}&\dots&\text{a}_{nn}\end{pmatrix},\text{a}_{\bar{ \text{u}}}=\begin{cases}0,\text{ Node i is not connected to node j}\\ 1,\text{ Node i is connected to node j}\end{cases} \tag{23}\]  
Furthermore, this study addresses the mutual coordination of highway grades by segmenting the highway network into a multi-layered structure comprising main roads, secondary roads, and branch roads. A multi-layer highway network model is constructed to elucidate the connections and node coupling relationships among the various layers of the network [26]. Utilizing road network modeling, the delivery path problem is conceptualized as an issue of node arrival within the established topological relationships. In the event of disturbances to the road network, certain nodes and edges may become inoperative. Consequently, the subsequent step involves implementing specialized processing for these affected components.