Abstract:     At present, China′s industry is facing double pressure at home and abroad. Accelerating promotion of the innovation-driven strategy is the inevitable choice for China to get rid of the constraints. However, limited by the foundation of innovation and the level of openness, there are obvious inter-regional differences in industrial innovation output in China. Moreover, inter-regional technological exchanges and knowledge spillovers are also insufficient, which hinders the improvement of overall innovation level. How to strengthen the regional innovation connection and build a regional collaborative innovation community has become a difficult problem for China′s industry to overcome. Since industrial production activities in any region cannot be carried out separately from other regions, the supply and demand relationships are the basis of inter-regional industrial spatial correlation. Along with production relationship, the innovation output will also overflow among regions. Therefore, if the inter-regional industrial innovation spillovers relationship is explored from the perspective of production relations, the inter-regional innovation spillovers can be increased quickly and effectively, which is of great significance to the formulation of inter-regional industrial collaborative innovation strategies.Considering the internal consistency of input-output technology and SNA method, this paper combines the two methods to analyze the spatial spillovers of industrial innovation from the perspective of production relations. First, this paper merges the industrial sectors in the input-output tables of 30 provincial-level regions in China to obtain the inter-regional industrial input-output table. And on this basis, the spatial spillovers of industrial innovation based on the supply relationship and demand relationship is measured. Then, this paper adopts the social network analysis method to construct the industrial innovation spatial correlation networks based on the supply and demand relationships. Finally, this paper analyzes the structural characteristics of innovation networks in two directions, and adopts the QAP method to reveal the main causes of spatial correlation of industrial innovation.Through above analysis, it can be concluded that: (1) Through the analysis of the overall structure characteristics of the networks in two direction, it is found that although the regional industries have established increasingly close and stable innovation linkages based on production relations, the density of the innovation networks in two directions is lower than 0.5 in the five research years, indicating that the degree of innovation spatial correlation is low and needs to be strengthened. The innovation spillovers issued by various regions have always been balanced while the flow of innovation spillovers has become more centralized, meaning that the level threshold of innovation networks has become more obvious. (2) Through the analysis of the status and role of each region in the networks, it is found that in the network based on the supply relationship, 8 provincial-level regions such as Beijing, Anhui and Chongqing play the central role. They act as intermediaries in the innovation relations among other regions and can easily obtain innovation resources. Nine provincial-level regions such as Inner Mongolia, Liaoning and Fujian have low participation in the network and weak innovation relationship with other provinces. In the network based on the demand relationship, nine provincial-level regions such as Jiangsu, Anhui and Shandong are the key nodes, while ten provincial-level regions such as Beijing, Heilongjiang and Guangxi are on the edge. (3) Through the analysis of the regional spatial clustering characteristics and the roles of regional plates, combined with the innovation spillovers paths among regional plates, it is found that the innovation networks in two directions can both be clustered into four plates, playing three roles including beneficiary, broker and spillover. At the same time, there exist the agglomerations of regions with strong influence and that of regions with weak influence in the two networks, without obvious geographical division. Comparing to the weak internal links of four plates, the innovation spillovers among them are stronger. (4) Through the QAP correlation analysis, it is found that geographical proximity as well as the regional differences in R&D personnel, R&D funds, technology upgrading funds and foreign capital utilization are the main reasons for the formation of the spatial correlation of industrial innovation. From the perspective of evolution trend of influence, it can be seen that the influence of geographical proximity has a decreasing trend, while the influence of R&D personnel, R&D funds, technology upgrading funds and foreign capital utilization have increased. The other factors all have little influence on the spatial correlation of industrial innovation, and are only significant in a few years. Among them, regional differences in the level of industrial development can strengthen the spatial correlation of innovation based on the supply relationship while weaken that based on the demand relationship. The regional differences in economic development level, infrastructure and marketization level can strengthen the spatial correlation of industrial innovation in two directions.Based on the above empirical conclusions, this paper puts forward targeted and detailed policy recommendations, in order to provide reference for optimizing inter-regional industrial production relations, promoting the spatial spillovers of industrial innovation and building regional industrial collaborative innovation community.

Key words: spatial correlation of industrial innovation, supply relations, demand relations, social network analysis method, QAP method