Complex network characteristics of the planned subway station network in Hangzhou (2005-2022)

. The complex network characteristic of the planned subway station system is of great significance to the centrality layout of the existing urban areas. The three phases of the Hangzhou subway plan from 2005-2022 are selected as a case, and the complex network analysis method is used to study the centrality characteristic of the planned subway station system. The study found that with construction, the network density, clustering coefficient, average shortcut distance, all centrality indicators of the network gradually decreased; but in phase Ⅲ adjustment, the average shortcut distance, three centrality potential indicators have all rebounded substantially. The newly-added airport rail express line has greatly increased the overall cohesion of the original subway network. The subway station networks of five planning stages all have smaller clustering coefficients and larger average shortcut distances, but none of them have a small-world characteristic, and the scale-free characteristic is still not obvious.


Introduction
As an effective urban development model for the coordinated development of transportation and land use, Transit-Oriented Development (TOD) has attracted the attention of many countries in the world and has been carried out active practices. However, many urban managers often lack overall strategies in the spatial development of metropolitan areas, especially in the urban spatial structure, land use, and public transportation integration [1] . Since we hope to see the effect of policy implementation soon, we pay more attention to the rapid construction of public transportation infrastructure to solve mobility problems, while neglecting the integration with land use to guide the sustainable and livable development of the city [2] . Hangzhou urgently needs to conduct targeted research on its urban space environment in response to the requirements of TOD, so as to realize the coupling of the built environment and large-scale public transportation.
As a theory describing the interrelationship of nature, society, and engineering technology, the complex network method provides a new perspective for studying the structural characteristic and functioning laws of real network systems. The central feature is the research focus of complex network analysis, which reflects the importance of the role played by individuals in an organization or system. Many researchers have abstracted road systems, public transportation systems, subway systems, etc. into complex network models, and developed several studies, such as structural features [3][4] , central features [5][6] , and land use and urban economic activities [6][7][8] . Li Jin et al. [3] , Zhang Tieyan et al. [4] studied the complexity and scale-free characteristic of subway networks; Huang Yong et al. used complex network analysis methods to analyze the overall, partial, and individual structural characteristic of the complex network of public transportation [5] ; Paolo Crucitti et al. studied the centrality and statistical distribution characteristic of the transportation network of 18 cities in the world [6] ; Wang Fahui, etc. studied the relationship between the transportation centrality of Baton Rouge and land use density in the United States [7] ; Sergio Porta et al. studied the central characteristic of the Barcelona transportation system [8] . The above research reveals the character of the complex network of the transportation system and its interaction with urban land use from different levels and provides an important reference for people to deeply understand the coupling mechanism of public transportation and the built environment.
However, it should be pointed out that the existing research is more focused on the road system, while the research on the subway station system is insufficient. This study selects the three phases of the Hangzhou subway plan from 2005-2022 as a case study, using complex network analysis methods to study the centrality characteristic of planned subway stations based on topological network structure, which will help the making decisions based on the TOD development advantages, potentials and differences and provide a scientific basis for the formation of an urban organic renewal strategy at the stage of stock optimization.  (Table 1). Phase Ⅲ

Research objects and scope
301 Line 1-10 224 Phase Ⅲ (ADJ) 302 Indexes such as betweenness centrality potential, closeness centrality potential, degree centrality potential are important indicators to measure the centrality of the overall network (Table 2). UCINET software can measure the network centrality characteristic, which was developed by Stephen Borgatti, Martin Everett ， and Linton Freeman of the University of California, Irvine.

Indicators
Meaning Betweenness centrality potential The betweenness centrality of the overall network Flow betweenness centrality potential The flow betweenness centrality of the overall network Closeness centrality potential The closeness centrality of the overall network Degree centrality potential The degree centrality of the overall network 3 Research results According to the phased plan, the number of subway lines and stations is gradually increasing. From the first phase to the phase Ⅲ adjustment, the overall subway network has increased from 2 to 11 lines, and the number of stations has increased from 56 to 237. In this process, the network density and clustering coefficient indicators gradually decreased; while the average shortcut distance gradually increased, but there was a substantial decrease in the 5th phase ( Figure 1, Table 3). The betweenness centrality potential, flow betweenness centrality potential, closeness centrality potential, degree centrality potential all show a gradual decrease with the progress of stages. However, in the phase Ⅲ adjustment, in addition to the flow betweenness centrality potential, the other three centrality potential indicators all showed a significant increase, of which the intermediate central potential and the close to betweenness centrality potential and closeness centrality potential increased significantly (Figure 2).

Complex network characteristics
A complex network refers to a network with some or all of the properties of self-organization, self-similarity, attractor, small world, and scale-free. Its main characteristics include small-world, scale-free, and other characteristics. The small-world characteristic reflects the convenient connectivity of complex networks with a large number of nodes and the average shortcut distance is small; while the scale-free characteristic reflects the serious heterogeneity of complex networks, and a small number of nodes often have a large number of connections while most of the nodes have few connections. The degree distribution of the nodes conforms to the power-law distribution. The comparison method of Watts et al. [9] and the Small Worlds Quotient method of Davis et al. [10] can be used to determine the small world attributes of the network. The subway network models in the five planning stages all satisfy L real ＜L ran ＜L reg , but none of them satisfy C ran ＜＜C real ＜ C reg ; at the same time, the small world quotient is far less than 1 (Table 4). Therefore, none of the subway networks models in all the planning phases has small world characteristic.
Regarding the scale-free characteristic, it can be determined by using the cumulative probability distribution of each node and the natural logarithm distribution of the cumulative probability of each node. In double logarithmic coordinates, the power-law distribution is represented by a straight line whose slope is the power exponent. Taking the phase Ⅲ adjustment of the subway plan (Phase 302) as an example, the fitting coefficient of the fitting equation of the cumulative point probability distribution of the overall network is 0.8445 when the power-law distribution is considered. And the fitting coefficient is 0.9129 when the polynomial distribution is considered. considering the linear distribution. And the fitting coefficient is 0.9713 when considering the polynomial distribution. The above results indicate that the cumulative point-degree probability distribution of the overall network during the phase Ⅲ adjustment is closer to a polynomial distribution than a power-law distribution (Figure 3). At the same time, the long tail phenomenon is not obvious from the distribution of actual points. Therefore, the scale-free nature of the subway network at this stage is not obvious. In the same way, the scale-free characteristic of the other four stages is not obvious. Compared with the Beijing, Guangzhou, and Shanghai subway networks as of the end of 2011, although the subway network of Hangzhou has a similar scale, it has a larger average degree, a shorter average shortcut distance, and a larger average clustering coefficient which show a better network characteristic (Table 5).