**6. Results and Discussion**

The main purpose of the experimental study is to investigate the properties of an urban public sustainable transportation network and optimize it. Complex network theory was used to construct the neighboring site-type undirected network model. An urban sustainable public transportation network was optimized based on the betweenness. The urban transit network's properties were

evaluated by complex network theory and related methods, and the possibility of optimization was formulated as Equations (8)–(20), with a solution procedure. Weaker sustainability gives rise to quite a lot of problems in the current urban transit system. Therefore, sustainable development should be highlighted when conducting the optimization of public transport networks. In the experiments, we analyzed three scenarios. First, the optimization model based on the betweenness centrality helped cut down the path length and improved sustainability. Second, the constraints of a single line and the overall line network were analyzed and compared. Finally, the Dijkstra algorithm in an effort to easily obtain an effective solution and its implementation steps were analyzed. Sustainability analysis was embedded in the above scenarios and discussed in the following.

(1) In the results of the network analysis, the degree distribution of the bus transportation network in Xi'an was uneven, showing obvious polarization. The number of nodes with intensity below 10 was 2215, accounting for 78.9% of the all nodes, and the proportion of nodes with intensity above 52 was nearly 1.1%. High valuable sites are often assumed to be important transfer hub functions. Thus, they deserve to be the focus of construction, and the surrounding road surface needs to be widened as well. Traffic congestion will accordingly be reduced and the speed of bus traffic will be improved.

(2) From the average path length, the average value was 28.445. The maximum value was 80. The results mean that residents of Xi'an travel about 28.445 bus stops on average when taking a bus. By contrast, the maximum value of path length for the Shanghai bus network is only 32, and the average value is 7.585; while the maximum for Beijing is 103, and the average is 17.3866. As for such large cities as Shanghai and Beijing, the number of bus stations is several times more than that of Xi'an, and the average path length is smaller than that of Xi'an, indicating that the bus systems in these two large cities are more developed than the Xi'an bus network. Although the average distance of Beijing bus stations is smaller than that of Xi'an, the bus number in Beijing is three to four times larger than that in Xi'an. On the other hand, the scale of Chengdu's public transport network is similar to that of Xi'an, but the average path length is 10.81, which is smaller than that of Xi'an. It can be seen from these data that the average path length of the bus network in Xi'an is relatively large, which is closely related to the lack of public transportation routes to the outer suburbs and the unreasonable layout of Xi'an bus lines, which means that the convenience of Xi'an citizens is not high. What is more, the convenience of citizens also depends on the traffic flow and non-linear coefficient. The non-linear coefficient refers to the ratio of the actual traffic distance between the starting points of the road and the linear distance between the two points.

(3) The clustering coefficient was used to describe the aggregation of nodes in the network, that is, how close is the network. The average clustering coefficients reflect the intensity of the bus lines in the entire bus network. The clustering coefficient of each station in the Xi'an bus station network was calculated, and the values of 1934 stations were found to be 0, indicating that there are many neighboring stations in Xi'an that are not connected with each other. As the clustering coefficient of the station is relatively low, the connection between its neighbors is sparse, and most of the traffic between these neighbors has to pass through the station, resulting in its heavy load. Thus, stations with a high clustering coefficient are more likely to be blocked than stations with a low clustering coefficient. The number of stations with a high clustering coefficient in the bus network of Xi'an is small, and only 208 of them have clustering coefficients of 1 or above. Therefore, the average clustering coefficient of the whole network is not high, which is 0.223. However, it is higher than that of Shanghai and Beijing, which is respectively 0.064 and 0.14. This indicates that the bus lines in Xi'an are relatively denser.

(4) The betweenness characterizes the influence of nodes or edges on the entire network, and has a strong practical significance for solving real network problems. The betweenness of the Xi'an bus station network was calculated. The bus stations with larger betweenness were compared. It was found that the larger betweenness and number of bus lines passing through were not correlated. Increasing the traffic and bus throughput performance of these nodes had a very significant effect on improving the operational efficiency of the entire network. Thus, the urban sustainable transportation network optimization model was established and solved based on betweenness.

(5) From the data visualization results, we found that one of the most obvious features of the Xi'an bus lines was that the lines are too long. The lines pass across three districts or even more to connect the urban center to the suburbs. Long-distance travel cannot ensure full loads and so decreases the sustainability of the routes. In experiments we found that the line detour time can be reduced when the regular bus lines were shortened. The regular buses in the suburban–urban–suburb areas should be adjusted to the suburban–suburban and suburban–urban edge as much as possible. By such a method, the sustainability of the bus lines and tours can be improved. At the same time, some small-bus routes leading to the outer suburbs are considered to be restricted to enter the urban area and just reach the bus hub in the suburbs. This can reduce the repeated and disorderly crossing of buses, and reduce the occupation rate of buses on major roads, thereby reducing traffic congestion and improving the overall operational efficiency and sustainability of the public transportation system.

(6) We also considered the network resilience in the experiment analysis by simulating node failures and through time. That is to say, it was able to provide and maintain an acceptable level of service in the face of faults and challenges to normal operation. A local failure of the network will increase the burden on other parts of the network, especially the key nodes and branch lines. Their faults are likely to cause the entire network to collapse. Congestion and its spread have a greater impact. The overall stability of the public transport network is robust and fragile due to its heterogeneity in scale-free performance. The key nodes and branch networks play a vital role in the connectivity of the entire network, reflecting the complexity and intrinsic dynamics of the public transport network. Relevant literature [15,17] also confirms that improving the capabilities of key nodes and the micro-circulation capability of the feeder roads is an important approach for improving the overall network capabilities.

(7) From the perspective of complex networks, it is feasible to split the central hub, so that the work originally undertaken by one node is decomposed into several interconnected nodes, and the synchronization capability of the network is significantly enhanced. This feature is also tested by visualization and simulation upon the network. When the bearing capacity of the original single station is weakened, a new station can be set up at intervals of about 100 m, and the bus lines that are docked can be diverted to reduce the queue waiting for the bus, which can enhance the network transportation capacity.
