**7. Remarks and Conclusions**

Complex network theory offers meaningful ideas for urban transit network studies. With the extensive development and application of the theory, increasingly more scholars are interested in deep study on complexity of transportation engineering. Urban transportation network design and optimization requires a combination of application and actual operation. It should not be limited to the topological structure analysis, instead, a concentration on the guidance of planning and design should be highlighted. The ultimate purpose is to actually improve the efficiency and sustainability of the network and society.

Firstly, this study used the complex network theory method and conducted a practical study on the urban transit network in Xi'an. The topological properties of the network were investigated and showed some insights into the public transportation network.

Secondly, a betweenness-based model and solution method was developed to improve the public transportation network's sustainability.

Thirdly, discussions on the features of the Xi'an transit network were presented. Some problems of public transportation were discovered from the perspective of sustainable development.

Urban traffic network structures have numerous impacts on traffic congestion and related challenges. Apart from network design optimization, possible directions of future policy could help maintain the network and avoid potential problems. First, the governmen<sup>t</sup> should clarify the principle of prioritizing the development of public transportation and enhancing the ability of public transportation to lead the city's development. Second, infrastructure construction needs

to be highlighted. In the bus hub station, charging facilities and other supporting facilities ought to be equipped to facilitate the use of trams. Simultaneously, the connection between urban public transportation and other modes can be strengthened to improve interchange efficiency. Third, investment in intelligent bus systems should be stressed and the application of information technology in urban public transportation operation management, service supervision, and industry managemen<sup>t</sup> should be promoted. Guidance on improving information sharing and resource integration of urban public transportation and other modes needs to be strengthened. Fourth, measures incorporating urban logistics into urban transit are to be encouraged. With online shopping and e-commerce growing tremendously, express delivery vehicles are crowding urban traffic. In case some urban transit facilities are not well utilized, they can be used to share some urban logistics contributing to less traffic congestion.

To sum up, this study constructed the bus transit network of Xi'an, analyzed the topological characteristics of its complex network, and proposed an optimization model based on betweenness centrality and policy guidance. However, further research should be carried out considering the weight and directionality of the edge, the traffic flow, and robustness. Additionally, a novel trend combining complex network theory and data mining will be prospected. Furthermore, due to data acquisition problems, we could not obtain the flow data at each leg between any pair of bus stations in each bus line; we also did not use the spatial properties of the bus stations and attached communities. When we are able to obtain the related data, the limitations of this study will be further studied. First, the optimization procedure will be improved to consider the above origin–destination flow and spatial data. Second, the sustainability instruments will be examined by considering the impacts of node and edge dynamics on the network's structures. As so the infrastructure, development strategies will be tested upon the network. Third, due to the openness of the study on network optimization, interviews and grounded studies will be conducted as a base of network simulation and analysis.

**Author Contributions:** Conceptualization, G.-L.J., R.-G.M. and Z.-H.H.; Methodology, G.-L.J. and Z.-H.H.; Software, G.-L.J. and Z.-H.H.; Validation, G.-L.J. and R.-G.M.; Formal Analysis, G.-L.J.; Investigation, G.-L.J.; Resources, G.-L.J.; Data Curation, G.-L.J.; Writing-Original Draft Preparation, G.-L.J.; Writing-Review and Editing, G.-L.J. and Z.-H.H.; Visualization, G.-L.J.; Supervision, R.-G.M.; Project Administration, Z.-H.H.; Funding Acquisition, G.-L.J.

**Funding:** This research was funded by the National Nature Science of China, gran<sup>t</sup> number 71871136 and 71471109, the Science and Technology Committee of Shanghai, gran<sup>t</sup> number 16040501800, the Science and Technology Committee of Shaanxi, gran<sup>t</sup> number 2015SF296, and the Nature Science Foundation of Shaanxi gran<sup>t</sup> number 2017JM5104.

**Acknowledgments:** The authors are thankful to the reviewers for their constructive comments which helped improve the paper's quality.

**Conflicts of Interest:** The authors declare no conflict of interest.
