Abstract:    With the rapid development of the new scientific and technological revolution, innovation activities are constantly breaking through the boundaries of regions and organizations and becoming a multi-level and complex system engineering. The collaborative innovation process between enterprises and universities is a process in which knowledge elements are continuously combined to realize knowledge creation. In order to obtain knowledge and resources related to innovation, the cooperation scope of enterprises and universities have spread from the same administrative region to different regions. Hence, how to give full play to the advantages of innovation subjects to improve regional innovation ability, resource sharing and value co-creation is of vital importance.
    The social network theory holds that the subject is embedded in the interdependent network, and resource sharing and flowing in the network are important sources of continuous innovation. And interdependent multi-layer network is developed in the analysis method of social network. It refers to the network with different levels where different network nodes and different connections at each level, and there are connections between nodes at different levels. As far as we know, cross-regional industry-university collaborative innovation is the cooperative innovation behavior carried out by knowledge reorganization between enterprises and universities that belong to different regions. So, there is a cross-regional industry-university collaborative innovation network that composed of regions, knowledge elements and relations, which is a interdependent multi-layer network.
    It is creative to research enterprises, universities and knowledge elements of different regions in the same frame by using the method of interdependent multi-layer network. Meanwhile, it is conducive to integrating high-quality knowledge resources, so as to optimize regional innovation layout reasonably and improve the overall innovation capacity of the region and country. The research on this topic not only enriches the theoretical research in the field of multi-layer social network, but also provides valuable management enlightenment for the sustainable collaborative development of industries, universities and governments in the region.
   In this paper, a multi-layer network of cross-regional industry-university collaborative innovation in China is constructed by using the cross-regional patents applicated by the industry and university during 1997-2017 in China. Among them, the regional cooperation network is formed by region (31 provinces in China) as the node, and the cooperative relationship between regions is the connection. And the regional knowledge network is formed by region and knowledge elements (the front four digits of IPC classification number) as nodes, and the combination relation between knowledge elements is the connection. Further, the dependent variable of this paper is the cross-regional industry-university collaborative innovation performance of each province, that is, the total number of invention patents applied by the patent applicant in each province every year. The independent variables are the centrality and structure hole of cooperative network, and the diversity and combination opportunity of knowledge network. At the same time, Gross Domestic Product (GDP), number of "Double First-class" universities (U) and marketization index (MKT) of each province in China are taken as control variables. Based on the above, this paper constructs the time-fixed negative binomial regression model.
    The empirical analysis results indicate that the cooperative network and knowledge network act independently and jointly on cross-regional industry-university collaborative innovation performance, which verifies the hypothesis proposed.
First of all, the advantage positions of the region in the cooperative network influence cross-regional industry-university collaboration innovation performance and have significantly positive impacts on it. However, the location of the region in the cooperative network includes centrality and structure hole. It can break through the cooperation link between different regions, promote the circulation and use of heterogeneous resources in a wider range, and is conducive to the formation of innovative results.
    Secondly, the quality resources of the region in the knowledge network influence cross-regional industry-university collaboration innovation performance and have significantly positive impacts on it. Because when knowledge diversity and combination opportunity of knowledge network is better, the regional knowledge foundation is comprehensive and solid, which is conducive to the formation of new knowledge or competitive knowledge to realize cross innovation.
    Finally, the regional cooperative network and knowledge network affect the cross-regional industry-university collaborative innovation performance collectively. Specifically, the knowledge diversity negatively moderates the influence of the centrality and structural hole of cooperation network on cross-regional collaboration innovation performance while the knowledge combination opportunity negatively moderates the influence of the structural holes of cooperation network on cross-regional collaboration innovation performance. On the one hand, under the high-level diversity of knowledge network, the region has a wide range of knowledge fields. And then the excessive knowledge and resource load lead to redundancy innovation capital and disperse personnel investment in the region. Otherwise, under the low-level diversity of knowledge network, the regional knowledge field is single and thin. And then, the specialized knowledge and resources are conducive to deepening the exploration in the specialized field and forming the unique competitive advantage of the region. On the other hand, under the high-level combination opportunity of knowledge network, there are many connections between knowledge elements, and the willingness of knowledge reorganization is stronger than that of obtaining resources through cross-regional cooperation. Otherwise, under the low-level combination opportunity of knowledge network, there are few connections and combination possibilities between knowledge elements. And then, there is a strong motivation to obtain innovation resources through cross-regional cooperation, so it is more likely to form cooperative relations with other regions to produce innovation results and improve innovation performance.
    Based on the above research conclusions, this paper puts forward suggestions for the behavior of different innovation subjects. Firstly, the enterprises and universities between regions should strengthen the sense of cooperation and establish rich and direct cooperative relations through projects and alliances. Then the cooperation path between innovation subjects can be shorten and the innovation efficiency can be improved，which is conducive to realizing innovation resource sharing and value co-creation. Secondly, the region should expand the knowledge field by means of technology reproduction or talent introduction, and create unique and competitive knowledge resources to provide inexhaustible impetus for innovation. Thirdly, the government should play a guiding and service role in cross-regional collaborative innovation. It is meaningful for regions to encourage cooperation between different regions and different subjects by establishing effective cooperation platforms, mechanisms and norms, so as to create conditions for the subjects to form cooperative relations and produce innovative results.

Key words: interdependent multi-layer network, cooperation network, knowledge network, cross-regional industry-university collaboration innovation