4.2.4. Betweenness

The betweenness of node is defined as the number of shortest paths passing through a node in the network, reflecting the impact of the node on the network. It is calculated that the minimum betweenness of the bus station in Xi'an is 0, the maximum is 1,283,175.750, and the average is 54,134.063, Figure 4 shows the betweenness value of different nodes.

**Figure 4.** Node betweenness of the Xi'an public transit network.

A bus stop with a high betweenness is close to the topology of many other sites. It is usually a more important bus transfer site and has a greater influence in the network. As can be seen from Table 3, the betweenness and the number of bus routes that have passed are seemingly not correlated. In the planning of public transportation, it is necessary to recognize the importance of high degree or high betweenness sites, and improve the passenger flow and vehicle throughput performance of these stations, which have a very significant effect on improving the entire public transportation efficiency.


**Table 3.** Bus stops with high betweenness and passing routes.

A bus stop with a high betweenness is close to the topology of many other sites. It is usually a more important bus transfer site and has a greater influence in the network. As can be seen from Table 3, the betweenness and the number of bus routes that have passed are seemingly not correlated. In the planning of public transportation, it is necessary to recognize the importance of high degree or high betweenness sites, and improve the passenger flow and vehicle throughput performance of these stations, which have a very significant effect on improving the entire public transportation efficiency.

### **5. Sustainable Transit Transportation Network Optimization**

Research on the application of complex networks in public transportation systems showed that a scale-free network (BA network) has more adaptability. A few nodes have large degrees and the distribution of betweenness is not even. Links with high betweenness are responsible for the main passenger flow transportation, and are normally the public transportation hub points in the L-space public transportation network. The general bus congestion is also gathered on the links with high betweenness. The solution may focus on optimization of these key links. So, in order to solve urban public transportation congestion and maximize the capacity of the network, it is better to adopt the scale-free network topology structure. Whether in early planning or in later optimization, the corresponding driving mechanism can be used and the scale-free network topology developed to increase the capacity and sustainability of transportation networks.

The bus network optimization model is developed based on complex network theory. The complex network topology parameter is set as the objective, with the constraints of evaluation index of real bus network.
