**1. Introduction**

Urban transit transportation plays an important role in the sustainability of the economy, environment, and even the whole society, as it helps to improve traffic resource efficiency and effectively alleviate the contradiction between traffic supply and demand [1,2]. In particular, reasonable network structures contribute to reduce road congestion, travel difficulties, and related environmental problems such as air and noise pollution [3,4]. With the reduction of traffic congestion, a lot of energy and non-renewable resources can be saved, and traffic accidents, related deaths and injuries, direct and indirect economy losses can be avoided [5,6].

Although the contributions of urban transit transportation to sustainability are significant, the holistic construction of a public transportation system for many cities is seriously lagging behind [7,8]. Especially, with the increasing number of private cars, the proportion of transit transportation has declined and been replaced by other modes with low resource utilization ratios. It therefore results in increasing travel time by public transportation and lowering the service level of it. This problem is extremely obvious in China, where the proportion of people choosing public transportation in the world's major developed cities is between 45% and 60%, while that in China is less than 30% [9].

The methods in the realm of complex networks and systems are well developed and applied in transport systems. System dynamics as an important branch of system science was used to consider the transportation supply and demand dynamic balance and their interaction with urban development [10]. Due to the comprehensive consideration of sustainability problems, modern control theory has been applied in the fields of transportation [11,12]. The former has applicability and superiority in dealing with complex interactions, especially urban traffic complexities. The latter plays an important part in transportation managemen<sup>t</sup> control. These two methods inspire systematic studies on urban transit transportation networks.

An urban public transport network can be viewed as a complex system of the urban transport system and socio-economic environment. Both the transportation department administration and professional scholars are working hard to explore how to improve the performance of the system, so that it can provide transportation services that are smooth, convenient, and environmentally friendly [5]. Urban transit transportation networks present the characteristics of complex systems. Complex network theory is a favorable method for studying complex systems. It emphasizes the topological nature of system architecture; complex networks provide a theoretical approach to the study of complexity [13,14]. Complex theory based on multidisciplinary knowledge can be used to study the complexity of urban transit transportation networks, so a network's space–time complexity and evolution mechanism can be explored. It provides theoretical guidance for the scientific planning of urban public transport structures. Complex networks highlight the topological characteristics of the system structure. Because the geometric properties of complex systems play a primary role in the network's dynamic behavior, public transportation can be depicted by traffic flows on complex networks involving bus lines and docking stations. Therefore, the advantages and disadvantages of the public transport network's structure have greatly affected the efficiency of passenger transportation in the entire public transport system. The topology of the public transport network deserves further research. By analyzing the characteristics of the existing network, a better public transportation system can be designed, and thus its utility can be improved [15,16].

Research on the complexity of urban transportation networks generally focus on the structural characteristics of transportation networks' topology. Additionally, it is increasingly important to analyze the impact of network structure on traffic. Different urban transportation networks may call for specific theoretical guidance for planning, design, and management. Research on these areas help to explore general rules and special features for different types of cities. Evolutionary mechanisms of urban transportation networks can be achieved, and the time and space complexity of networks can be explored [5].

In summary, the research on urban public transport networks' complexity is still in its early stage. Although the research on urban public transport network models have provided the basic statistical characteristics of the network, the models rarely consider the spatial features of the transit transportation network. This study looks at the urban transit network's topology features from the perspective of complexity, measures the hierarchical relationship of nodes in the network, develops an optimization method based on complexity features presenting an effective method to improve the utilization rate of the urban public transport system, cut down traffic congestion, and reduce environmental pollution. The Xi'an urban bus network was chosen for its representation. Due to the presence of historical reasons, the layout of the road network in Xi'an is believed to be unreasonable. The population in the central area of the city is dense; the distribution of the population and road space is extremely uneven; the construction of transportation facilities is restricted; and the transit network has serious structural defects [17]. Additionally, the total construction of the public transportation system is seriously lagging behind, and the proportion of the structure is out of balance. Compared with other developed and advanced large cities around the world, Xi'an, as a new rising first-tier large city in China, is going to achieve a large increase in economy and transportation which means the public transportation is going to face challenges as well. How to optimize the network structure and make it consistent with economic and social development is not only meaningful and valuable for Xi'an, but for similar urban transportation systems around the world.

The rest of the manuscript is organized as follows: Section 2 presents a review on related studies; Section 3 introduces the methods used for urban transit network properties analysis; Section 4 explains the data sources and network construction images, and presents the urban public transportation network's features; Section 5 focuses on the formulation and optimization of the sustainable public transportation network design. Section 6 demonstrates the discussions on improvement of sustainable public transportation networks. Finally, conclusions and further research prospects are presented in Section 7.
