Overall characteristics of the network
The Density of urban innovation associated network is measured by density tool of software Ucinet. The results show that the overall connection of Chinese urban innovation correlation network is not strong, and the connection efficiency is low. Among them, the network density value is 0.084. It indicated that the overall network density is low, which reflects the low degree of innovation connection among cities. The average path length and the average clustering coefficient are measured by the software Gephi, respectively 3.083 and 0.630. It indicated that the Each city needs an average of three intermediary cities to achieve the connection, and the number of redundant innovative contact channels is large, which leads to low contact efficiency. Compared with innovation networks of the same scale, the average path length and average clustering coefficient of Chinese urban innovation correlation networks from the perspective of HTZs are larger, and the accessibility of the overall innovation network is poor.
Hierarchy characteristics of the network
Based on the innovation connection strength value, the overall mean value is taken as the truncation threshold. And the connection strength value larger than the mean value is taken as the basis to indicate the existence of innovation correlation between cities, so as to construct the innovation correlation directed network. In addition, XY to Line operation in ArcGIS10.2 was used to connect two cities, and quantile method was further used to divide the connection strength value into four levels for visual expression (Figure.1). The results show that the network hierarchy is clear, and Beijing, Shanghai and Shenzhen are always the core hubs of the network at all levels. The overall spatial pattern of the four-tier innovation correlation network with "Z" as the main axis is presented.
The first-level connection strength threshold is (47,3346. The first-level network takes the central city as the leader of the innovation connection network, and constructs the innovation connection framework structure of the urban agglomeration. Most of these central cities are municipalities, provincial capitals or sub-provincial cities, and enjoy special policy environment and institutional advantages. With Beijing, Shanghai and Shenzhen as the core hubs, innovative links within the Beijing-Tianjin-Hebei region, Yangtze River Delta and Pearl River Delta city clusters respectively. However, there are some differences among the three regions: the performance of urban innovation connection in the Beijing-Tianjin-Hebei region is scattered; On the contrary, in the Pearl River Delta region, due to the compact urban layout, the urban innovation connection is more dense. The Yangtze River Delta region shows the innovative and collaborative development among three provinces and one city. In addition, the innovation connection between the urban agglomeration in the middle reaches of the Yangtze River (Wuhan →Changsha, Wuhan→Nanchang) and the Chengdu-Chongqing economic circle (Chongqing→Chengdu) also belongs to the first-level network。
The second-level connection strength threshold is (18,47. It extends more eastern and central region connections at the primary level. Apart from continuing to expand the scope of their respective radiation around the provincial capital cities, the innovative links between the cities across the provinces have also begun to emerge. The Hubei, Jiangxi and Hunan regions have gradually established connections with the cities in the eastern region (Wuhan → Zhengzhou, Hefei → Nanchang), and together with the Beijing-Tianjin-Hebei region and the Yangtze River Delta region constitute the "Z-shaped" eastern triangle connection framework. In addition, innovative connectivity connecting cities in the southwest to Guizhou (Chongqing → Guiyang) and connecting cities in the Northeast (Changchun → Harbin) was also formed.
The third-level connection strength threshold is (21,40. In the eastern region of the third-level network, the urban innovation network connection is gradually complex and dense, and the "Z-shaped" network pattern takes shape. The connection in the eastern region shows the form of overall dispersion and local agglomeration. In contrast to the sparse inter-city innovation connections in the western region, the core cities in the western region have weak radiation power, loose and isolated innovation connections, and the innovation correlation network structure has not yet emerged. With Shanghai and Shenzhen as the vertex and throughout the Yangtze River Delta, Pearl River Delta and the Middle reaches of the Yangtze River, the "Z" shaped in southern triangle has basically taken shape.
The fourth-level connection strength threshold is (7,10. The fourth-level network is the basis of China's urban innovation correlation network, and the lightning-like spatial pattern with the "Z" shape as the main axis appears. Different from the first three levels of urban innovation connections based on geographical proximity between central cities, the fourth-level network is the level with the lowest connection intensity, but the largest scale, and majority points to long-distance non-proximity connections between marginal cities. In the fourth-level network, the Z-shaped network with the Beijing-Tianjin-Hebei region, the Yangtze River Delta, the middle reaches of the Yangtze River and the Pearl River Delta as the core has more dense innovation connections among nodes inside the region than outside the region. However, owing to the lack of support for the overall network in Chengdu-Chongqing region and high-level innovation connection with the Middle reaches of the Yangtze River and the Pearl River Delta urban agglomeration, the overall structure failed to form a "diamond" structure of the network pattern.
Node centrality characteristics
Degree Centrality, Betweenness Centrality, and Closeness Centrality are measured with the Centrality tool in the software Ucinet. The results show that the centrality of urban degrees in the eastern region is higher than that in the western region, and Betweenness Centrality of the core cities in central China plays an important bridging role, and the cities located in remote areas close to the center are vulnerable to the influence of related cities.
In terms of Degree Centrality, cities in eastern regions are generally higher than those in western regions. The ranking of Degree Centrality of Beijing and Shanghai indicates that these regions are in the center of the network because they are most associated with other cities and have the greatest impact on the innovation efficiency of other cities. The point-in degree of Hefei, Nanjing, Wuhan and other cities is higher than the point-out degree, indicating that the spillover effect of the above cities is obvious. The point-in degree of Zaozhuang, Suqian and Xuzhou is lower than the point-out degree, indicating that the external radiation capacity of these cities is weaker than that of receiving external radiation capacity.
In terms of Betweenness Centrality, the core cities in the central China play an important intermediary role. Wuhan, Hefei, Xi'an and other central cities have the top three intermediary centers, and are far higher than other cities. It shows that these cities are the key nodes of the regional innovation connection network, play the role of the "bridge" in the network, and have a strong control role in the innovation connection between the cities. In addition, it is worth noting that the intermediary center degree value is 0 in Xining, Qiqihar and Yuxi cities. These cities are located in remote areas and have not yet played an intermediary role in the network.
In terms of Closeness Centrality, Closeness Centrality ranking varies from Degree Centrality and Betweenness Centrality. Nanchang, Hangzhou and Zhengzhou rank high in Closeness Centrality, and have a short shortcut distance with other cities in the innovation connection network, which can more easily transfer the innovation elements. Urumqi, Yulin and Ankang ranked low in Closeness Centrality, and had a long shortcut distance from other cities in the network, so it was difficult to transfer innovative elements. Shanghai and Beijing rank high in the inner Closeness Centrality and have the greatest influence on other regions, which is mainly due to superior innovation location conditions. The outer Closeness Centrality of Yinchuan and Shizuishan ranks the top, indicating that the above areas are greatly affected by other cities. This is because the remote areas have less innovation correlation, and innovation resources only come from neighboring cities, which are easily affected by related cities.
Cluster characteristics in cyberspace
Firstly, the Concor algorithm (iterative correlation convergence) in software Ucinet is used for cluster analysis of urban innovation associated network. The urban innovation correlation network can be divided into 8 third-level subgroups and 4 second-level subgroups. The four subgroups at the secondary level are divided into four innovation aggregation subgroups, namely, the northern hinterland subgroup, the eastern coastal subgroup, the southern region subgroup and the western cooperative subgroup. By calculating the average innovation quality index and centrality of each innovation condensation subgroup (Table.3), it can be seen that there are a large number of cities in the northern hinterland and southern regions of the subgroup, and the centrality of the eastern coastal subgroup ranks the first, while the western cooperative subgroup lags behind.
In terms of city number, the northern hinterland and the southern regions cover the largest number of cities, while the eastern coast and the western collaboration subgroups are small, only accounting for 36% of the total number of cities. In terms of quality of innovation, the average innovation quality index of cities in the eastern coastal subgroups was 2051.14, significantly higher than that of the other three subgroups, and the innovation development in other regions was relatively balanced. This is due to the gathering of many universities and scientific research institutions in eastern China, which has obvious talent advantages and innovative resource endowment. In terms of centrality, the average Degree Centrality of the eastern coastal subgroup is 47.31, which is five times the average degree degree of the last ranked western cooperative subgroup. The Degree Centrality of the northern hinterland subgroup and the southern region is relatively close. Among them, the point-in degree of the eastern coastal subgroup is greater than the point-out degree, showing an obvious innovation "spillover effect". On the contray, the point-in degree of the subgroup in the northern hinterland and the southern region is greater than the point-out degree, forming a "siphon effect". Influence by these, a large number of innovation factors such as knowledge, technology and talent flow out of the western region. Compared with other subgroups, the eastern coastal subgroup and the southern subgroup have higher intermediate centrality, because the Yangtze valley and South China have developed economic foundation and accessible high-speed rail network, and have better geographical advantages of bridging cities within other subgroups. The eastern coastal subgroup and the northern hinterland subgroup have a higher degree of Closeness Centrality, which has a strong attraction and influence on cities in other regions, and a wider range of innovation radiation, which can more quickly and directly relate to the inner cities of the subgroup.
Secondly, the Cohesion tool in software Ucinet was used to measure the internal E-I index of the subgroup and analyze the internal clustering characteristics of each subgroup (Figure.2). The results show that the northern hinterland subgroup, eastern coastal subgroup and southern regions subgroup all show small group network phenomenon, while the network characteristics are not obvious. The eastern coastal subgroup and the western cooperative subgroup are the "central actors" and the "marginal actors" respectively. The E-I index of the western collaboration subgroup is close to -1, reflecting that the density of the interurban network within the subgroup is higher than that outside the region. The reason is that the lack of cities with strong radiation and driving effect, and it is difficult to master the dominant connection with other cities, so it is independent of the overall innovation network. The E-I index of the northern hinterland, eastern coastal subgroups and southern regions is all positive. However, the absolute value of the E-I index of the northern hinterland and eastern coastal subgroups is low, indicating that the innovative connection of the subgroups are mainly derived from the subgroups themselves. Although the E-I indexes of the two innovative condensate subgroups are close to 0, the reasons are different: the eastern coastal subgroup E-I index is closer to 0, indicating that the urban network connection density within the region is close to the external network connection density. Driven by the radiation of Shanghai's strong core city, and with the support of the high-speed transportation network in the Yangtze River Delta urban agglomeration, the administrative constraints lead to the weakening of the boundary effect, which better integrates the regional network with the overall innovation network. The E-I index of the northern hinterland sub-group is slightly higher than that of the eastern coastal subgroup, indicating that the phenomenon of small groups in the Beijing-Tianjin-Hebei region is more significant, and the trend of innovation and integration in the Yangtze River Delta urban agglomeration is more obvious. The E-I index of southern region subgroup is closest to 1, and compared with the other subgroups, the innovative association network connection occurs more outside the region, and the internal network density is lower than the external network density. The reason lies in the fact that the Pearl River Delta urban agglomeration has promoted the interaction of inter-city innovation resources and inter-city innovation connection through the proximity of Hong Kong, Shenzhen and Guangzhou.
Analysis of the influencing factors
Model building
In the traditional regression analysis method, the autocorrelation of the relationship matrix structure will make the test of the significance of variables invalid. Here, the QAP analysis for relationship data is adopted to explore the influencing factors of urban innovation correlation network in China46. QAP regression analysis method(Quadratic Assignment Procedure, secondary assignment procedure) is a non-parametric test based on the replacement of matrix data. It is often used to reveal the regression relationship between one matrix and multiple matrices and can avoid multicollinearity without being independent of variables47. In order to further explore the mechanism of urban innovation correlation in China, the reference scholars discuss the view of "local frontier-global pipeline" and the discussion on the relationship between multidimensional proximity and innovation. In the view of "local frontier-global pipeline", local frontier refers to the frequent and continuous interaction and cooperation between adjacent innovation subjects, which is conducive to innovation in the same region. Global pipeline refers to the long-distance exchange fusion relationship between different countries, which facilitates the acquisition of heterogeneous knowledge from different environments and the diffusion of knowledge in the cluster48 ~ 52. In the thesis of proximity, the concept of multidimensional proximity of the French proximity kinetic party is gradually expanded, proposing geographical proximity, institutional proximity, cognitive proximity, cultural proximity, technological proximity, organizational proximity, and social proximity53. However, due to the different research objects and spatial scales, the influence mechanism of multi-dimensional proximity on innovation is controversial. Compared with the innovation subjects of micro-enterprises, the urban-scale innovation connections are more affected by geographical proximity, institutional proximity and cognitive proximity16. Among them, geographical proximity refers to the spatial division or proximity between subjects. Geospatial proximity is conducive to industrial interaction, personnel communication, information exchange and communication and cooperation between innovation subjects, and improves the efficiency of technical cooperation54. Institutional proximity refers to the similarity of the subject under informal constraints and formal rules. Cognitive proximity reflects the consistency of cognitive understanding of innovative subjects during communication20. Therefore, from the multidimensional proximity and urban economy and innovation, opening, select spatial adjacency, government administrative rank, industrial structure, economic development, opening, science and technological investment and innovation output difference is closely related to urban innovation seven factors as independent variable construction influence Chinese urban innovation association network structure, urban innovation association matrix (IA) as the dependent variable, to further reveal the influencing factors of Chinese urban innovation link. Accordingly, the regression model was constructed as follows:
IA = f (Geo, Ins, Ind, Eco, Ext, Sci, Inn) ༈2༉
The independent variables in Eq. (2) are described as follows: ①Spatial adjacency (Geo). The geographic adjacency matrix is constructed by measuring the geographic proximity with the adjacency dummy variable (0,1). The adjacent cities are denoted as 1, or 0 otherwise. ②Administrative rank of government (Ins). The administrative rank of the government is used to measure the institutional proximity between cities. If the administrative rank is the same, the value is 1, indicating that the administrative power is similar; otherwise, it is 0, so as to construct the administrative rank difference matrix.③Industrial Structure Differences (Ind). Based on the proportion of tertiary industry in gross regional product as the proxy variable of industrial structure, the difference matrix of industrial structure between cities is constructed to depict the cognitive proximity. ④Economic Development Differences (Eco). The per capita GDP is used as the difference matrix of economic development and the proxy variable of economic development.⑤Opening to the outside world difference (Ext). We will measure the degree of opening up by the proportion of total imports and exports to GDP, and build a difference matrix of opening up. ⑥Technology Investment Differences (Sci). The proportion of science and technology expenditure in the local general public budget expenditure represents the degree of urban support for innovation, so as to construct the difference matrix of science and technology investment. ⑦Innovation output difference (Inn). The number of patents is used to represent the level of innovation output and build the innovation output difference matrix. Referring to the method of constructing the difference matrix in the study of Wang Qingxi and Qin Qi et al. 55,56: Firstly, each unit is set as the ratio of the independent variable attribute in the city. Then, the independent variable matrix is binarized, and the threshold values of the above 5 difference matrices are respectively 1.2, 1.5, 1.2, 1.0 and 1.5, that is, the value is 1 if it is greater than the threshold value, otherwise the value is 0. Finally, the difference matrix of the binarized independent variables is obtained.
QAP analysis
The QAP correlation analysis of the correlation matrix of urban innovation in China was conducted by Software Ucinet, and the number of random substitutions was set to 10,000 times to obtain the correlation coefficient and significance level between the dependent variable matrix and various influencing factors (Table.4). The results showed that the correlation coefficient of spatial neighbor relationship, government administrative level, opening to the outside world and science and technology investment difference passed the 1% significance level test, and the difference of innovation output passed the 5% significance level test, indicating that the above independent variables had a significant correlation with the innovation association between cities. The differences in industrial structure and economic development did not pass the significance test, and it was preliminarily determined that the differences in industrial structure and economic development had no significant influence on the establishment of inter-city innovation correlation
According to the regression results, the spatial proximity relationship, administrative rank difference, industrial structure difference and opening to the outside world difference passed the significance level test of 1%, and the standardized regression coefficient of spatial proximity relationship was much higher than other factors. The difference in science and technology investment passes the significance level test of 5%, and the difference in economic level passes the significance level test of 10%.
From the perspective of multidimensional proximity, the absolute value of the regression coefficient of spatial proximity (Geo) is large and positive, indicating that geographical proximity plays a role in promoting urban innovation association. Spatial adjacency reduces the spatial obstruction of innovation communication and weakens the positive externality of knowledge spillover. As for the cities in the western cooperative subgroup that are far away from each other, they need to overcome greater distance friction in the transmission of innovation elements and technological exchange and interaction, so it is difficult to form a strong innovation connection. The coefficient of administrative rank difference (Ins) is significantly negative, indicating that institutional proximity is negatively correlated with innovation cooperation. The reason may be that local protectionism generates institutional costs in innovation cooperation between enterprises, thus hindering cross-regional innovation links. For example, Daqing of Heilongjiang Province in Northeast China and Tonghua of Jilin Province are both general cities in terms of administrative level. The industry of Daqing involves petrochemical, automobile and equipment manufacturing, while Tonghua is dominated by pharmaceutical industry. However, due to administrative barriers in inter-provincial innovation cooperation, even though there are industries with high industrial correlation between cities, strong innovation connection has not been formed. The industrial structure difference (Ind) coefficient is significantly negative, indicating that the similarity of perceived proximity between cities has a positive effect on innovation linkages. Strong innovation linkages are more likely to occur between cities with similar economic strength and industrial structure. However, it is difficult for Changzhi, Ordos and other cities dominated by the secondary industry to form an industrial environment for innovation and development in the short term, and they cannot form a strong innovation connection with Shanghai, Guangzhou and Shenzhen and other cities dominated by the tertiary industry.
From the perspective of economic science and technology innovation and opening up, economic level difference (Eco) is positively associated with urban innovation association, and the difference of opening to the outside world (Ext) is positively correlated with the dependent variable matrix. The difference of economic development and opening-up degree leads to the different pricing of innovation factors among cities. The price of innovation factors in economically developed coastal areas is often high, which directly leads to the flow of innovation factors from coastal cities with low marginal rate of return to inland cities with high marginal rate of return, thus bringing about technological interaction and knowledge flow between cities. The science and technology investment difference (Sci) is positive. It indicates that the science and technology investment difference is conducive to the construction of innovation connections between cities. The science and technology investment of central cities is usually the highest value in the region, and the central cities promote the formation of strong innovation connections within the region through the "siphon effect" of surrounding cities. For example, the proportion of science and technology expenditure in the regional of Wuhan and Nanchang, the central cities of the urban agglomeration in the Middle reaches of the Yangtze River, the general public budget is about two to three times that of the surrounding general cities. The high investment in science and technology in the central cities attracts the surrounding regions to carry out innovative exchanges and interactions with them. Innovation output difference (Inn) did not pass the significance test, indicating that the index of the number of patents granted has no significant influence on the establishment of innovation correlation.
Robustness test
In order to further test the robustness of the QAP regression results, by referring to the research method of Sun Zhongrui et al30, 80% and 120% of the mean value of the dependent variable of the urban innovation correlation matrix are selected as the threshold, and different binarization matrices of urban innovation correlation are constructed as the new dependent variable matrices, and QAP regression analysis is conducted with the aforementioned seven independent variable matrices. Robustness test was conducted by comparing the results. It is found that neither the coefficients nor the significance of the same independent variable matrix changed significantly under the two thresholds, which indicates that the influence factor matrix explained the independent variable matrix well, and the regression results were more robust and credible.