Abstract:    With the implementation of "innovation-driven development strategy", innovative elements such as talents, capital and information have flowed freely and efficiently among cities. The spatial structure of China′s economic development is undergoing profound changes, and central cities and urban agglomerations are becoming the main spatial forms of the development elements. Collaborative innovation in urban agglomerations is a process of knowledge creation through constant combination of internal knowledge elements, with cities as carriers, industries, universities and research institutes as innovation subjects. Therefore, it is very important to clarify the advantages of innovation subjects and the influence mechanism of urban agglomeration network, so as to rationally optimize the innovation layout of urban agglomeration and improve the overall innovation ability of regions and countries. According to the social network theory, there is knowledge search and cooperation behaviors across city boundaries in the process of collaborative innovation, and the knowledge flow in the network realizes continuous innovation. Innovation subject is essentially a collection of knowledge elements, and the process of collaborative innovation by innovation subject is also a process of reorganizing knowledge elements and forming a knowledge network to create new knowledge. Therefore, there exists a knowledge network composed of knowledge elements belonging to cities and their combination relations, and a cooperation network composed of cities and their cooperation relationships in the process of collaborative innovation of urban agglomeration. Both of them present a multi-layer network structure of dependency, which together affect the performance of collaborative innovation. We put industries, universities and research institutes and knowledge elements in different cities into the same framework for research based on the perspective of dependency multi-layer network. And the research of this topic not only enriches the theoretical research of urban agglomeration and multi-layer social network, but also provides valuable management enlightenment for collaborative innovation of urban agglomeration. In this paper, a multi-layer network of collaborative innovation in Yangtze River Delta urban agglomeration is constructed by using the patent application of industries, universities and research institutes in 2009-2018. Among them, the cooperation network is constructed by 41 cities in the Yangtze River Delta urban agglomeration as nodes, and the cooperation relationship between cities as a link. Knowledge network is constructed by cities and knowledge elements (the first 4 digits of IPC classification number of joint patent application) as nodes, and the combination relationship between knowledge elements as a connection. Furthermore, the dependent variable of this paper is the collaborative innovation performance of each city. Because innovation is an uncertain process, we use a three-year time window to obtain an average innovation output index. The independent variable is the diversity and combination opportunity of knowledge. The regulating variables are centrality, structural hole, central potential and network density of cooperative network. Meanwhile, GDP, R&D, teacher, MKT, capital, membership are the control variables. Based on the above analysis, we select a negative binomial regression model. The empirical analysis results show that the collaborative innovation network of urban agglomeration plays an important role in collaborative innovation performance, which verifies the proposed hypothesis. First of all, the high-quality knowledge resources in the knowledge network affect the collaborative innovation performance, and have a significant positive impact on it. When a city has diversified knowledge resources with high combination opportunities, it provides a chance for the city to establish a new connection of knowledge elements, which is beneficial for the city to acquire, integrate and absorb new knowledge for collaborative innovation. Secondly, the characteristics of knowledge network and the location of cooperation network jointly affect the collaborative innovation performance of urban agglomeration. Specifically, the centrality of cooperative network positively regulates the impact of knowledge diversity and knowledge combination opportunities on innovation performance, while the structural hole of cooperative network negatively regulates the impact of knowledge diversity and knowledge combination opportunities on innovation performance. On the one hand, the central city can contact a wide range of innovative resources through a large number of direct connections. And it has an advantage in identifying the distribution of innovative knowledge, thus absorbing new knowledge and reorganizing existing knowledge at a lower cost. On the other hand, cities occupying structural holes bring direct costs for them to acquire non-redundant knowledge, which hinders the absorption and utilization of diverse knowledge by cities, and thus is not conducive to collaborative innovation. Finally, the joint influence of cooperative network location and knowledge network characteristics on collaborative innovation performance of urban agglomeration is also influenced by cooperative network characteristics. Cooperative network density positively readjusts the moderating effect of cooperative network centrality on knowledge network characteristics and collaborative innovation performance, while negatively readjusts the moderating effect of cooperative network structural hole on knowledge network characteristics and collaborative innovation performance. The positive trend of cooperative network centrality readjusts the moderating effect of cooperative network centrality on knowledge network characteristics and collaborative innovation performance. On the one hand, there are a lot of connections between cities in high-density network, which improves the efficiency and flow speed of knowledge transfer and reduces the innovation cost, thus strengthening the positive adjustment of centrality and weakening the negative adjustment of structural holes. On the other hand, the connectivity in the high central potential network depends on some cities, which is conducive to the formation of a sound standard of cooperation and the promotion of knowledge flow. Therefore, it can strengthen the positive adjustment of centrality and weaken the negative adjustment of structural hole.Based on the above research conclusions, we put forward some suggestions for collaborative innovation of urban agglomeration. Firstly, the government should break down cooperation barriers and integrate innovative resources. Talent introduction and project combination can be used to realize efficient utilization and reorganization of diversified innovative knowledge. Secondly, the government should optimize the network layout and establish a long-term cooperation mechanism. The construction of leading cities and core cities in urban agglomerations can play their leading and radiating role, and then establish a benign development cooperation order. Finally, the government should improve the connectivity of urban agglomerations and build advantageous industries. Measures such as improving infrastructure and creating cross-city and inter-provincial cooperation projects can encourage the establishment of collaborative innovation cooperation between cities.

Key words: collaborative innovation of urban agglomeration, dependent multi-layer network, knowledge network, cooperation network