## 3 Methodology and Data
### Study Area and Data Sources
These data, covering a range of socioeconomic events, ensure the broadness and representativeness of the data. Consequently, it is utilized to construct a directed and weighted information network. (2) Investment data of listed company: As a comprehensive financial data platform, Tushare (accessed on 1 June 2021, [[https://tushare.pro](https://tushare.pro)]([https://tushare.pro](https://tushare.pro))) provides a wide range of financial data services. As of the end of 2019, a total of 3777 companies were listed on the Shanghai and Shenzhen stock exchanges. This study obtained the registered locations of these listed companies, their shareholders, and the number of shares held using the Tushare financial data interface. Non-individual shareholders' registered city information was filtered and collected, and the investment capital of each shareholder was used as the weight for the investment network relationships, constructing a directed and weighted investment network. (3) High-speed rail operation data: To ensure the comprehensiveness of traffic contact intensity, considering the traffic flow on different dates, high-speed rail (G, D, C) schedule data was obtained from the official China Railway 12306 website ([[https://www.12306.cn/index/](https://www.12306.cn/index/)]([https://www.12306.cn/index/](https://www.12306.cn/index/))) for 23 days from September to November 2019, which included 17 weekdays and 6 non-working days/holidays. An average of 7071 train services per day was recorded, with the data for train services between sample cities retained. The number of train services between cities was  
Figure 3: Study area. Base map source: State Bureau of Surveying and Mapping, GS(2020)4619, with no modifications to the base map. used to represent the strength of the transportation connections, and an undirected, weighted high-speed rail network was constructed using the P-space network construction method. (4) Highway network data: According to a circular jointly released by the National Development and Reform Commission and the Ministry of Transport about the national road network, the China Transportation Technology Database ([[https://www.transformcn.com](https://www.transformcn.com)]([https://www.transformcn.com](https://www.transformcn.com))) provided data on the built sections of the national highway network from 2013 to 2030, including the starting and ending points, cities/counties passed, interchanges along the route, and exits. The highways passing through the sample cities were used to represent the connection relationships between cities, and an undirected, weighted highway network was constructed using the P-space network construction method. Additionally, this paper uses the China Statistical Yearbook (2017 to 2019) to obtain socioeconomic data of the cities, including permanent resident population and GDP for empirical analysis. These data provide a comprehensive perspective on the development status of the cities, enhancing the representativeness and credibility of the research findings. Through these rigorous data collection and network construction methods, this study ensures the representativeness of the data. Based on the intercity relationship data, this study constructs four types of urban networks to describe information flow, capital flow, human mobility, and infrastructure connectivity among cities. The urban networks to be analyzed are denoted as \(G_{t}=(V,E_{t},W_{t}),t\in\{I,C,R,H\}\), where \(V\) represents the sample cities selected in this study; \(E_{t}\) represents the edge relationships between sample cities, varying by network type; and \(W_{t}\) represents the weight of intercity relationships, also varying by network type. Specifically, they are as follows:  
(1) Information network, \(G_{t}\): \(s_{ij}\) represents the annual average search index from city \(i\) to city \(j\). If \(s_{ij}>0\), an edge \(e_{ij}\in E_{t}\) is established with weight \(w_{ij}=s_{ij}\), \(w_{ij}\in w_{t}\).