Abstract:     Collaborative innovation can realize the sharing of advanced technology and the complementation of advantageous resources among different subjects, and can effectively reduce the risk brought by the uncertainty of single-subject innovation, this is of great significance for guiding innovation activities, allocating regional innovation resources rationally and improving regional innovation ability. Beijing-Tianjin-Hebei regional urban agglomeration is an important link in the regional economic ties among Beijing, Tianjin and Hebei, and a major carrier of coordinated innovation. It enjoys good conditions for development and strong policy support, but the innovation output is still restricted by such problems as the flow of innovation factors and the gathering of necessary resources, such as knowledge and information. To study the regional collaborative innovation network of Beijing, Tianjin and Hebei Region, and to study the impact of the structure and multi-dimensional proximity of the collaborative innovation network on the network, this is particularly critical to enhance the ability of Beijing, Tianjin and Hebei region to co-ordinate innovation and drive regional economic growth through innovation.Based on the data of joint patent application in Beijing-Tianjin-Hebei region from 2006 to 2020, this paper constructs a regional collaborative innovation network in Beijing-Tianjin-Hebei region. By using social network analysis (SNA), this paper analyzes the structure of collaborative innovation networks, and tests the necessity and adequacy of the five adjacent dimensions that influence the collaborative innovation networks in Beijing-Tianjin-Hebei region, a quadratic assignment procedure (QAP) regression model was constructed to study the effect of five adjacent dimensions on the evolution of collaborative innovation networks. The research shows that the cities in the Beijing, Tianjin and Hebei region are more and more closely connected, and the capacity of the largest node to absorb resources and obtain information has no significant change compared with other nodes in the three stages, co-innovation networks meet the small-world characteristics of the Beijing, Tianjin and Hebei regional co-innovation networks, with Beijing and Tianjin occupying the first and second core positions respectively, the status, control ability and autonomy of the nodes in the collaborative innovation network show different gradients and have been improved in the past ten years. The proximity of space transaction costs is the necessity and sufficiency that affects the Beijing, Tianjin and Hebei regional collaborative innovation network, while the other proximity dimensions are the sufficient and unnecessary conditions that affect the Beijing, Tianjin and Hebei regional collaborative innovation network. The impact of spatial transaction cost proximity and geographical proximity on the Tianjin Hebei regional collaborative innovation network gradually decreases, the effect of technology proximity on the regional collaborative innovation network in Tianjin, Hebei and China is significant and inverted U-shaped, the impact of social proximity and institutional proximity on the regional collaborative innovation network in Beijing, Tianjin, Hebei is gradually increasing. Based on the above findings, this paper puts forward several suggestions on network structure and network evolution for the development of Tianjin Hebei regional collaborative innovation network.Compared with the existing research, the innovation of the paper lies in: first, in the research method level, the scholars use the traditional econometric regression research method to assume that regions are independent of each other, there is no recognition of the possible spatial correlation of transaction costs, and there is a lack of a unified analytical framework to integrate transaction costs and collaborative innovation into the same system. In this paper, the temporal global principal component analysis is used to measure the spatial transaction costs in Beijing-Tianjin-Hebei region. The csQCA truth table algorithm is used to analyze the data to obtain the logical possible coverage and consistency scores, to verify that the spatial transaction cost is the necessity and sufficiency that affects the Beijing-Tianjin-Hebei region regional collaborative innovation network, and to study the significance of the spatial transaction cost proximity to the collaborative innovation network. Secondly, at the theoretical level, scholars study the influence of geographical proximity on collaborative innovation networks from the perspective of geo-economics, however, from the perspective of space transaction cost, technological economy, sociology and institutional economy, the different adjacent dimensions will have different impacts on the collaborative innovation network. Based on the multi-dimensional proximity theory, this paper regards the spatial transaction cost, technology, geography, social and institutional factors as proximity, the influence of multiple adjacent dimensions on the evolution of the Beijing-Tianjin-Hebei region regional collaborative innovation network was analyzed by using quadratic assignment procedure(QAP) regression, which can realize the significance test between "relationship and relationship".

Key words: Beijing-Tianjin-Hebei region, collaborative innovation network, multidimensional proximity, necessary and sufficient condition, quadratic assignment procedure (QAP)