**2. Literature Review**

Complex network theory can be used to capture and describe the evolutionary mechanisms, laws and functions of systems by means of graph theory and some statistics methods [13,18]. At the end of the 20th century, the study of complex network theory was no longer limited to the field of mathematics. Scholars began to consider the overall characteristics of a large number of actual networks with complex connections. Two groundbreaking articles have been recognized as the beginning of a new era of complex network research. One is entitled "Collective Dynamics of 'Small-world' Networks" [19]. The other is entitled "Emergence of Scaling in Random Networks" [20]. These two articles reveal the small-world characteristics and scale-free nature of complex networks, and establish corresponding models to illustrate the mechanisms of these characteristics. With the extensive research on complex systems, the research on the real world from various perspectives has spread to many disciplines and fields, such as cooperation networks in social networks, company directors' networks, research citation networks, language networks, and computer technologies networks, the neural network, the power network, telephone networks, and urban transportation networks, etc. [21].

Applying complex network theory to analyze the complexity of urban transportation network topology is a key to the study of complex urban transportation networks, and it is also one of the basic issues of urban transportation network research. It has been gradually realized that it is not enough to use some local data for traffic analysis and road planning to solve traffic congestion in cities. It is necessary to conduct a comprehensive analysis of the routes or the road network.

In recent years, research on weighted networks have been rapidly developed. Weighted networks introduce weight as a dimension to distinguish the difference between edges, as the strength between network nodes may be different. In 2006, Boccaletti [22] published the latest review on complex network research. Complex weighted networks can describe actual complex systems. At present, the research work on weighted networks mainly focuses on modeling research [23], complex characteristics [24], and dynamics on complex-weighted networks [22]. The results of some studies in many practical weighted networks have shown that vertex weight and edge weight also follow the power-law distribution. After giving weights to the connections, it provides a new method for characterizing the system. Adjusting the weights also provides a new means for optimizing the nature of the network and its functions. Complex networks are also important for the prediction and processing of emergencies. The network is found to be stable after the nodes are randomly deleted, but if the key connectivity nodes in the network are deleted, the network is easily destroyed [18].

Many scholars have conducted a lot of theoretical studies and empirical analyses of complex networks. The existing research mainly focuses on the empirical analysis of subways, streets, and public transportation networks, and studies the basic topology of the network, like the degree distribution, mean shortest distance, clustering system, etc. Latora and Marchiori carried out a preliminary study of the network characteristics of the Boston Metro [25]. Sen et al. studied the small-world characteristics of the Indian railway network [26]. Seaton et al. calculated the small world effect of the railway line network between Boston and Vienna [27]. Sienkiewicz analyzed the topological characteristics of the bus transportation network in 22 cities in Poland, and then further analyzed the clustering, match degree, and median characteristics of the Polish urban public transportation network [28]. The complex-weighted network has also received widespread attention in recent years. Li et al. [29], Bagler et al. [30], Barrat et al. [31], and Guimera et al. [32] studied the weighted network characteristics of airports in China, India, and the world, respectively. Among them, Barrat et al. [31] used real-world data to deeply explore the correlation between weights and topologies in weighted networks, and introduced the definition of some characteristics in weighted networks. Domestically, the complexity of urban transport networks has just begun. Wu and Gao [33] carried out theoretical and empirical research on complex networks earlier, and analyzed the scale-free characteristics of the Beijing public transport network. Wei et al. [34], Di [35], Zhao et al. [36], Zhang [17], and Zheng et al. [37] carried out empirical studies on urban transit transportation networks in Chengdu, Tianjin, and Xi'an based on complex network theory. These studies have shown that urban transportation networks have the structural characteristics of complex networks.

To sum up, although the research on networks has developed rapidly [38,39], it still faces many challenges in the study of urban public transportation. As far as urban public transportation is concerned, the existing research has just started, and there are still many problems to be solved. The characteristics of different network topologies need to be further analyzed. In particular, it is necessary to theoretically explore models that can optimize the network.
