# Identification of Critical Road Links Based on Static and Dynamic Features [PERSON]
## 3 Methodology  
### Directed Dual Traffic Network Constructing  
Most existing research on traffic network modeling typically represents intersections as nodes and the connections between intersections as edges. However, in the field of traffic, the road link plays a crucial role, serving as the primary location of traffic accidents and traffic control measures in traffic networks. To address this limitation, we construct a directed traffic road network model using the dual method [20], which preserves the connection and circulation relationships within the traffic network. Specifically, in this method, links are mapped as nodes, and the connection relationships between different links are represented as edges, while the circulation relationship of traffic flow between links is captured as connections. To capture the traffic demand and state in the city, we calculated the traffic flow and average speed of road links within a specific time interval. The directed dual traffic network is defined as follows:  
\[G=(V,E,S_{T},F_{T}) \tag{1}\]  
where \(V=\{v_{1},v_{2},\ldots,v_{n}\}\) is the set of link nodes which means the road links, and \(n\) is the number of road links. \(E=\left\{(v_{i},v_{j}),v_{i},v_{j}\in V\right\}\) is the set of edges in the network. \(S_{T}=\{s_{1},s_{2},\ldots,s_{n}\}\) is the set of average speeds of link nodes in a specific time interval \(T\). \(F_{T}=\left\{f_{1},f_{2},\ldots,f_{n}\right\}\) is the set of traffic flow of link nodes in a specific time interval \(T\). \(T\) is a constant, such as 30 min.  
Compared to the traffic network with the primal method, the directed dual traffic network emphasizes the significant role of links in the traffic system. The approach enhances the clarity of the topological relationship between different links. In the directed dual traffic network model, the static and dynamic characteristics of road links can be captured. The structure of the traffic network displays the connection relationship between different links, which depicts the static characteristics of road links. Meanwhile, the traffic flow and average speed of the road links reflect the dynamic characteristics of the traffic network. Where the traffic flow characterizes the traffic demand, and the average speed characterizes the traffic state. It is crucial to note that a small traffic flow during congested times may not necessarily indicate low traffic demand.  
Based on the connection relationships between road links in the directed road network, the original topology of the road network can be well represented as the directed dual traffic network. Figure 1 illustrates the original directed traffic network topology and its corresponding directed dual traffic network topology. In the figure, letters A-H represent different intersections, while numbers 1-7 represent different road links. The direction of the road links indicates the direction of traffic flow. For instance, in the original traffic network, road link 1 and road link 4 have a flow connection, whereas road link 1 and road link 2 do not. Consequently, in the directed dual traffic network, road link node 1 is connected to road link node 4, but not to road link node 2.