1 Introduction
Innovation has long been a cornerstone of national progress, driving scientific and technological advancements and embodying the essence of human achievement, particularly in the current phase of economic transition. For enterprises, innovation is not merely an option but a critical survival strategy in an increasingly competitive global market. As market dynamics become more unpredictable and the digital economy advances rapidly, companies find it harder to rely exclusively on internal resources for technological innovation. The rise of external collaboration has become essential for overcoming these limitations.
Empirical research underscores the role of collaborative R&D in helping firms transcend their resource constraints and leverage external knowledge, leading to what is now known as open innovation (Karamanos, 2016). In the context of open innovation, firms form collaborative networks by engaging with external partners, such as suppliers, customers, universities, and research institutions. These networks facilitate the exchange of resources and knowledge, helping companies overcome barriers to innovation. By actively collaborating, firms can co-develop technologies, access specialized expertise, and diversify their innovation portfolios, leading to more efficient and impactful innovation outcomes. In China, the increasing integration of enterprises with higher education institutions and government bodies under the triple helix framework (Jimenez et al., 2024) has become more prominent. These collaborations, which are accelerated by a country’s rapid economic growth and innovation-driven strategies, play a pivotal role in enhancing firm competitiveness. Enterprises positioned at the center of this model not only participate in market competition, but also serve as intermediaries. By collaborating with universities and governmental institutions, they can access cutting-edge research, talent, and policy support, thereby transforming these resources into commercially viable products and services. Proactively engaging in or embedding collaborative innovation networks and interacting with partners within these networks to access indispensable innovation-related resources, knowledge has become a foremost strategic choice for enterprises to augment their competitiveness (Cheng et al., 2022). Understanding the role of network intermediaries in collaborative innovation networks is crucial. These intermediaries facilitate knowledge flows, enhance connectivity among partners, and amplify innovation potential. Their positioning within the network can significantly influence firms’ innovation outcomes. This research explores how network intermediaries affect collaborative innovation performance in the context of Chinese listed companies. By examining the structural characteristics of these networks through social network analysis, we aim to unveil the intricate relationships between network properties and innovation performance.
In recent years, scholars have increasingly focused on the relationship between collaborative networks and enterprise innovation from two perspectives. First, they explored how network structural features influence inter-organizational collaboration or organizational innovation performance (Ruan & Chen, 2017). Commonly employed metrics, such as degree centrality (Kim & Fortado, 2022), betweenness centrality (Bloodgood et al., 2017), closeness centrality (Onder & Ulukan, 2020), pagerank centrality (Lau et al., 2020), and eigenvector centrality (Dong & Yang, 2016), reflect the degree of embeddedness of enterprises within the network structure.
Second, from the perspective of collaborative network relationships, scholars have investigated the impact of collaborative relationships on enterprise innovation, focusing primarily on the intensity and breadth of the relationships (Lin & Yang, 2020). For instance, Tsai et al. (2019) found that firms with stronger political relationships have more opportunities for innovation (Tsai et al., 2019). These studies have enriched our understanding of the relationship between network characteristics and enterprise innovation from a social network perspective, providing feasible strategic references for enterprises to engage in open innovation. However, a clear consensus regarding the relationship between network structure and collaborative innovation has not yet been reached. Some scholars argue that network centrality negatively influences enterprise innovation (Lyu et al., 2019). Furthermore, most studies treat networks as homogenous entities, overlooking the inherent heterogeneity of positions within the network. Different network positions exhibit substantial variations in resource acquisition, knowledge absorption, and partner selection (del-Corte-Lora et al., 2017).
Within inter-organizational technological collaboration networks, network intermediaries represent a unique structural position that inherently possesses advantages in information control and resource transmission. Social network theory suggests that nodes occupying intermediary positions tend to wield higher influence, which is often measured using betweenness centrality to reflect the degree to which a node occupies an intermediary role in the network. However, existing research has inadequately addressed this specialized network position of intermediaries, often treating network centrality as a unified construct. This has led to prolonged debates regarding the relationship between network positions and enterprise innovation. Additionally, scholars frequently overlook the interaction between network structure and relationship strength, which can significantly affect a firm’s open innovation performance. Understanding this interplay is crucial for optimizing resource and knowledge utilization within collaborative networks.
This study investigates how network intermediaries influence collaborative innovation performance among Chinese listed companies. Specifically, this research seeks to elucidate the mechanisms through which intermediaries facilitate or hinder innovation processes within collaborative networks. Understanding these dynamics is crucial for enterprises striving to optimize their innovation strategies amid increasing competition and resource constraints. This study builds upon existing literature by introducing a theoretical model that not only considers the role of network intermediaries but also incorporates the moderating effects of the network clustering coefficient and relationship strength. By exploring these factors, this research aims to clarify the complexities of network interactions and their implications for innovation outcomes. Therefore, the following section introduces the relevant literature background and the hypotheses of this research. We also present the data, variables, and research methods employed. Through empirical investigation and discussion of the results based on the collected data, we then provide managerial implications derived from the examination of our hypotheses.
2 Literature review and hypotheses
2.1 Network intermediary and collaborative innovation
The concept of network intermediary has garnered significant attention in the field of collaborative innovation (Lin & Wei, 2018). These intermediaries serve as strategically positioned entities within networks and play a critical role in shaping innovation outcomes by facilitating information exchange and knowledge transfer among various nodes (Katzy et al., 2013). For instance, Xu et al. (2019) found that organizations occupying intermediary positions enhance their innovation capabilities, thus underlining the importance of these nodes in fostering collaborative efforts.
From the perspective of social capital theory, intermediaries function as bridges connecting otherwise isolated nodes, thereby enhancing communication and collaboration within the network (Feranita et al., 2017). Liu et al argued that the core nodes of network intermediaries were mostly large organizations that were equipped with core technology (Liu et al., 2017). Their central position enables them to access diverse information and resources from various parts of the network and then redistribute them to their immediate contacts. This information brokerage fosters stronger relationships between partners, reduces transaction costs, and enhances the diffusion of innovative ideas. By leveraging their position, intermediaries can broker partnerships, encourage the exchange of complementary knowledge, and mediate conflicts, thereby enhancing cooperative dynamics within the network.
Additionally, the unique position of network intermediaries allows them to foster a culture of collaboration by bringing together diverse stakeholders, including competitors, suppliers, and research institutions. This diversity enhances the flow of ideas and perspectives that are crucial for innovation. Intermediaries can also identify and promote best practices, ensuring that the knowledge gained from collaborations is effectively utilized. Network intermediaries also play a crucial role in mitigating conflicts and facilitating negotiations, which can otherwise stifle innovation. Their ability to manage relationships and expectations helps create an environment conducive to open innovation, where firms feel more secure in sharing ideas and resources. In light of these insights, we formulated the initial hypothesis of this study:
H1: Network intermediary has a positive impact on firms’ collaborative innovation performance.
2.2 Moderating role of clustering coefficient
Previous studies have suggested that when innovative entities are embedded in highly clustered collaborative networks, they have the potential to access greater heterogeneity in social capital (Guan et al., 2015). This is attributed to the intensified connections between diverse entities, leading to increased collaborative opportunities. Unlike the measurement approach of network centrality, the clustering coefficient, another significant metric of network position, largely reflects the local features and degree of group formation within the network. A higher clustering coefficient is more conducive to the diffusion and propagation of knowledge and technology (Su et al., 2019). However, as the clustering coefficient of the network increased, the presence of structural holes in its position decreased. This indicates a network structure with high redundancy. In such densely interconnected clusters, intermediaries may find fewer opportunities to mediate between distant collaborators due to the prevalence of direct interactions within the cluster. This decreased mediation potential might hinder intermediaries’ ability to bridge gaps and facilitate novel knowledge exchange across different parts of the network, consequently weakening their impact on collaborative innovation performance.
In addition, the clustering effect can lead to an imbalance in the distribution of resources and opportunities. Firms within high-cluster networks may inadvertently prioritize collaborations with familiar partners, potentially sidelining innovative firms located outside these tight-knit groups. This behavior can result in a form of exclusion where valuable ideas and resources from less central, yet highly innovative firms go unnoticed. Traditionally, intermediaries have facilitated knowledge transfer and collaboration among diverse entities. However, when most interactions occur within a dense cluster, the role of intermediaries diminishes as they find fewer opportunities to broker connections that introduce novel knowledge. The intermediary’s capacity to act as a conduit for innovation becomes severely limited, which undermines the purpose of their position within the network.
In conclusion, although clustering can facilitate efficient information flow and foster collaboration, it also poses significant risks to innovation. The propagation of homogeneous knowledge can create an environment that stifles creativity, reinforces groupthink, and limits firms’ ability to adapt to new challenges. Thus, this study proposes the following hypothesis:
H2: The clustering coefficient negatively moderates the relationship between network intermediary and collaborative innovation performance.
2.3 Moderating role of collaborative relationship strength
In the context of collaborative networks, the strength of collaboration ties between entities plays a crucial role in determining the effectiveness of knowledge exchange and innovation outcomes (Cao et al., 2018). When collaboration ties are robust, partners are more inclined to share resources, insights, and knowledge, ultimately leading to more successful collaborative efforts. Strong collaborative relationships indicate frequent and substantial interactions that can significantly enhance the likelihood of generating innovative ideas and solutions. This perspective aligns with social exchange theory, which posits that parties engaged in strong, reciprocal interactions are more likely to share valuable resources and support one another (Yang et al., 2022).
Empirical evidence suggests that larger enterprises tend to forge extensive, tightly knit collaboration networks, while smaller and medium-sized enterprises typically maintain smaller, less interconnected networks (Liu et al., 2022). These differences highlight how the strength of ties can vary significantly based on organizational size and capability. Additionally, strong collaborative relationships are essential for enterprises aiming to achieve systematic and autonomous breakthrough innovations, particularly in dynamic market environments (Partanen et al., 2014).
By virtue of their central position, network intermediaries can enhance the flow of information between diverse entities, acting as bridges that connect disparate parts of the network. These intermediaries facilitate not only the exchange of knowledge but also the integration of diverse perspectives, which is critical for innovation (Wang & Wang, 2012). Entities linked by strong ties and guided by network intermediaries are better equipped to leverage diverse knowledge resources in their collaborative efforts. In scenarios of substantial collaboration, intermediaries amplify resource allocation efficiency, idea exchanges, and solution development.
Moreover, the presence of strong collaborative ties can amplify an intermediary’s effectiveness in fostering innovation. When entities are deeply connected, they are more likely to engage in open and meaningful exchanges, allowing for a more fluid transfer of knowledge and ideas. This collaborative environment fosters trust and reduces the risk associated with sharing sensitive information, further enhancing innovation capacity. Conversely, in weaker collaborative ties, the potential for resource sharing and knowledge diffusion diminishes, leading to missed innovation opportunities. In summary, the strength of collaborative relationships plays a pivotal role in shaping the dynamics between network intermediaries and collaborative innovation. Thus, this study proposes the following hypothesis:
H3: Collaboration strength positively moderates the relationship between network intermediary and collaborative innovation performance.
The theoretical model used in this research is shown in Figure 1.
Figure 1. The theoretical framework of the research. |
3 Research design
3.1 Data
The object of this study is publicly listed A-share industrial enterprises. Through meticulous exploration and data retrieval from the Incopat official website (https://www.incopat.com), we amassed a comprehensive collection of patent application data spanning 2006 to 2020. Incopat is a global intellectual property database that is widely recognized for its extensive coverage of patent data, including but not limited to patents from China, the United States, Europe, Japan, and other major patent offices. The platform is equipped with advanced search tools that allow for the precise retrieval of patent information, making it a highly reliable source for innovation research. In this research, we used Incopat to search for patent applications based on multiple key fields, including firm name, patent title, application date, International Patent Classification (IPC) code, and legal status. This ensured a robust and relevant dataset. The accumulated dataset consists of a total of 64,521 patent records and 5,720 firms. Two main reasons can support this selection. First, in the current phase, China is undergoing the initial stages of digital transformation. Industrial enterprises have assumed a central role in digital economic development. Second, the technological innovation prowess of industrial enterprises holds significant significance for society at large. The objectivity, comparability, and practicality of patent data have granted them widespread utility within innovation research fields.
This study seeks to construct an enterprise patent network by focusing on patent data where the applicant type is “enterprise”, and the number of applicants is ≥2. Other incomplete patent records were excluded from consideration. The cycle of enterprises engaging in patented technology research and development is usually three to five years; then, we segment the patent data into rolling time windows of four years each. This allowed us to construct a technology collaboration innovation network for enterprises using patent applications from the preceding four years. After the arrangement, we obtained an imbalanced panel consisting of 62,196 joint patent applications. Table 1 provides an overview of the sample observations and network construction details. Notably, the network’s scale exhibits ongoing expansion over time, evident through linear growth in the average degree and average path length, indicating that as the network grows, node connections become looser. Moreover, an increasing average degree signifies the emergence of subgroups in the network, dividing the overall technology collaboration network into various sectors.
Table 1. The construction detail of collaborative networks. |
| Period | Firm | Patent | Ego-net | Network density | Average degree | Average length path |
|---|---|---|---|---|---|---|
| 2008-2011 | 261 | 1,614 | 85 | 0.007 | 1.862 | 1.563 |
| 2009-2012 | 332 | 2,226 | 98 | 0.006 | 2.066 | 1.667 |
| 2010-2013 | 368 | 2,970 | 108 | 0.006 | 2.109 | 1.688 |
| 2011-2014 | 422 | 3,842 | 122 | 0.005 | 2.199 | 1.873 |
| 2012-2015 | 489 | 4,782 | 135 | 0.005 | 2.585 | 1.940 |
| 2013-2016 | 556 | 5,615 | 144 | 0.005 | 2.712 | 2.178 |
| 2014-2017 | 643 | 6,732 | 158 | 0.004 | 2.734 | 1.887 |
| 2015-2018 | 766 | 9,215 | 175 | 0.004 | 2.851 | 1.913 |
| 2016-2019 | 886 | 11,506 | 190 | 0.003 | 2.756 | 2.273 |
| 2017-2020 | 997 | 13,694 | 204 | 0.003 | 2.776 | 3.093 |
3.2 Variables
3.2.1 Dependent variable
Collaborative innovation performance (PE) is a pivotal aspect of this study. Patents serve as a common metric for quantifying an enterprise’s innovation output. In this context, patent data is utilized to characterize technological innovation performance. Specifically, the quantity of joint patent applications submitted by enterprises during the current window period is used to measure collaborative innovation.
3.2.2 Independent variables
The explanatory variable in this study is the intermediary of enterprises, which also serves as a crucial indicator of node positioning in the network. Specifically, betweenness centrality (BC) is employed to quantify the intermediary role of enterprises within the network (Abbasi et al., 2012). BC measures the extent to which a network node i is positioned between two other distinct nodes j and k in terms of relationship pathways. This is expressed as the ratio of the number of shortest paths between any two distinct nodes that include i to the total number of shortest paths. It can be calculated as:
$ B C(i)=\frac{\sum_{j \neq k} \frac{g_{j k}(i)}{g_{j k}}}{(N-1)(N-2)} $
Where N represents the total number of nodes in the collaborative network, gjk denotes the total count of shortest paths between nodes j and k, and gjk(i) represents the number of paths that pass through intermediary node i in the shortest paths between nodes j and k.
3.2.3 Moderating variables
Two moderating variables were considered in this study. The first is the clustering coefficient (CL), a crucial metric for gauging the level of connectivity between different nodes in the network (Zhang et al., 2008). This reflects the extent to which the other distinct nodes connected to node i are mutually adjacent. Its formula is given by:
$ C L(i)=\frac{2 e_{i}}{k_{i}\left(k_{i}-1\right)} $
Here, ki represents the total number of neighboring nodes for the i-th node, and ei is the total number of edges between all neighboring nodes of the i-th node.
The second moderating variable is relationship strength (ST), which serves as a significant representation of the frequency of cooperative interactions between innovation entities. It measures the degree of close communication between a node and its collaborative partners. This study employs the ratio of joint patent applications with all partners to the total number of partners as a measure of relationship strength.
3.2.4 Control variables
We consider three control variables in this research.
The triadic closure structure (TR) refers to the formation of stable collaborative relationships between enterprises in a social network analysis. It is characterized by a cyclic structure within the network, where partners engage in stable and reliable connections that balance each other (Vedel & Servais, 2019). A higher count of triadic cooperative relationships signifies more stable collaboration between enterprises, fostering long-term performance enhancement.
Eccentricity (EC) refers to the maximum value of the shortest paths between a node and other nodes within a network (Li et al., 2009). It measures the breadth of the relationships of a network node: the larger the eccentricity.
Closeness centrality (CC) is another vital metric for gauging network node position. In a local individual network, a shorter sum of the shortest path lengths from one node to other nodes indicates higher closeness centrality (Lozares et al., 2015). It can be calculated as:
$ C C(i)=1 / \sum_{j=1}^{N} d_{i j} $
Here, dij represents the shortest path length between node i and other nodes j in the network, and N denotes the network size.
3.3 Methods
This research employs a combination of social network analysis (SNA) and negative binomial panel regression models as its primary analytical approaches. Social network analysis is a powerful tool for dissecting and understanding intricate relationships within a network (Zhou & Li, 2024). In the context of this paper, it serves as a tool to meticulously examine collaborative innovation networks among enterprises. Using social network analysis techniques, we calculated key network indicators, including betweenness centrality, clustering coefficient, closeness centrality, triadic cooperative relationships, and eccentricity. These network measures capture the non-linear interactions and structural positions of firms within the innovation network, providing a nuanced understanding of the role of network intermediaries in collaborative innovation. While social network metrics describe a network’s structure and relational dynamics, we further employ classical statistical techniques to assess the influence of these network characteristics on firm-level innovation performance. This mixed-method approach, combining the non-linear insights of SNA with linear regression models, is well supported in recent studies (Reck et al., 2022) and allows for a more comprehensive analysis of the relationships between network position and innovation outcomes. Specifically, network metrics derived from the topological structure of the patent collaboration network were incorporated into regression models as independent variables to evaluate their statistical impact on collaborative patent output.
Due to the highly discrete nature of enterprise patent application data, which represent the core variable, traditional linear regression models may not provide accurate results, leading to significant bias in estimating causal relationships. To address this, the study applies the negative binomial regression model, an extension of Poisson regression, which is particularly suited for count data with over-dispersion (when the variance exceeds the mean). In this paper, the dependent variable is the count of collaborative patent applications, with a mean of 29.73 and a standard deviation of 149.42, making the negative binomial regression an appropriate choice for handling the data’s high variability. The specific model can be expressed as:
$ \begin{aligned} \log \left(E\left(P E_{i, t}\right)\right)= & \beta_{0}+\beta_{1} \cdot B C_{i, t}+\beta_{2} \cdot C L_{i, t}+\beta_{3} \cdot S T_{i, t}+\beta_{4} \cdot B C_{i, t} \cdot C L_{i, t}+ \\ & \beta_{5} \cdot B C_{i, t} \cdot S T_{i, t}+\beta_{6} \cdot \text { Controls }+\varepsilon_{i, t} \end{aligned} $
4 The empirical study about impact of network intermediary on collaborative innovation
4.1 Descriptive statistics and correlation analysis
High correlation coefficients would suggest potential collinearity among variables. Table 2 presents the descriptive statistics, including the means and standard deviations. Table 3 presents the correlation coefficients of the variables. In conjunction with the above analysis, a Variance Inflation Factor (VIF) analysis was conducted. The VIF assesses the potential presence of multicollinearity among variables. Generally, VIF values below 4 or 10 are indicative of an acceptable absence of multicollinearity. In this study, the VIF values ranged from a minimum of 1.01 to a maximum of 3.17, well below the threshold of 10. Moreover, all inter-variable correlation coefficients were below 0.80. *, **, and *** indicate significance at 10%, 5%, and 1% levels, respectively. Therefore, it can be concluded that multicollinearity is not a concern among the variables in research.
Table 2. Descriptive statistics of variables. |
| Variable | Number | Mean | Standard Deviation | MIN | MAX |
|---|---|---|---|---|---|
| PE | 5,720 | 29.73 | 149.42 | 1.00 | 4,181 |
| BC | 5,720 | 10.41 | 98.71 | 0.00 | 2,612 |
| CL | 5,720 | 0.32 | 0.44 | 0.00 | 1.00 |
| ST | 5,720 | 8.86 | 24.01 | 0.20 | 692.00 |
| TR | 5,720 | 3.41 | 12.84 | 0.00 | 225.00 |
| EC | 5,720 | 2.05 | 1.37 | 1.00 | 9.00 |
| CC | 5,720 | 0.73 | 0.24 | 0.17 | 1.00 |
Table 3. Correlation results of variables. |
| PE | BC | CL | ST | TR | EC | CC | |
|---|---|---|---|---|---|---|---|
| PE | 1.000 | ||||||
| BC | 0.507* | 1.000 | |||||
| CL | 0.019 | -0.033 | 1.000 | ||||
| ST | 0.371* | 0.027 | -0.056* | 1.000 | |||
| TR | 0.640* | 0.374* | 0.203* | 0.060* | 1.000 | ||
| EC | 0.030 | 0.133* | 0.260* | -0.039* | 0.106* | 1.000 | |
| CC | 0.0222 | -0.068* | -0.279* | 0.024 | -0.081* | -0.832* | 1.000 |
*Indicates statistical significance at the 10% significance level. |
4.2 Regression results
The negative binomial regression model was used to analyze the influence of network intermediaries on collaborative innovation performance. Table 4 presents the regression results.
Table 4. Regression results of negative binomial model. |
| Variable | Collaborative innovation performance | ||||||
|---|---|---|---|---|---|---|---|
| M1 | M2 | M3 | M4 | M5 | M6 | M7 | |
| BC | 0.008*** | 0.001*** | 0.002*** | 0.002*** | 0.002*** | 0.004*** | 0.005*** |
| (0.001) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | |
| CL | 0.206*** | 0.208*** | 0.412*** | ||||
| (0.049) | (0.049) | (0.000) | |||||
| ST | 0.068*** | 0.069*** | 0.070*** | ||||
| (0.001) | (0.001) | (0.000) | |||||
| BC×ST | 0.001*** | 0.000*** | |||||
| (0.000) | (0.000) | ||||||
| BC×CL | -0.005*** | -0.006*** | |||||
| (0.002) | (0.000) | ||||||
| TR | 0.061*** | 0.057*** | 0.058*** | 0.049*** | 0.051*** | 0.046*** | |
| (0.002) | (0.003) | -0.003 | (0.001) | (0.001) | (0.000) | ||
| EC | -0.011 | -0.014 | -0.015*** | 0.126*** | 0.116*** | 0.110*** | |
| (0.025) | (0.024) | (0.024) | (0.019) | (0.018) | (0.000) | ||
| CC | 1.099*** | 1.127*** | 1.106*** | 0.952*** | 0.931*** | 1.066*** | |
| (0.140) | (0.139) | (0.139) | (0.102) | (0.102) | (0.000) | ||
| Constant | 2.083*** | 1.887*** | 1.815*** | 1.830*** | 0.473*** | 0.492*** | 0.271** |
| (0.021) | (0.146) | (0.146) | (0.146) | (0.109) | (0.000) | (0.012) | |
| N | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 |
| R2 | 0.023 | 0.055 | 0.055 | 0.056 | 0.177 | 0.179 | 0.183 |
*, **, and *** denote significant levels at 10%, 5%, and 1%, respectively. |
M1 serves as the baseline model, incorporating only the core explanatory variable and collaborative innovation performance. The main effect test results demonstrate that network intermediaries positively impact collaborative innovation performance for enterprises, and this impact is statistically significant at the 1% level. The results in M2 reveal that even after introducing control variables such as the clustering coefficient, eccentricity, and closeness centrality, the regression coefficients remain significant. Thus, hypothesis H1 is confirmed. This implies that in the context of technological collaborative innovation networks among industrial enterprises, occupying an intermediary position in the collaboration process contributes to improved collaborative innovation performance. Specifically, when enterprises assume the role of intermediary bridges in knowledge and technology exchange, they facilitate the establishment of platforms for technical and knowledge sharing. Consequently, other entities are more inclined to collaborate with platform-oriented enterprises, thereby enhancing the core company’s collaborative opportunities and innovation performance.
Furthermore, to explore whether other network structural features and relational characteristics act as moderating mechanisms between network intermediaries and collaborative innovation performance, we introduce the clustering coefficient and relationship strength as two moderating variables in addition to the baseline regression model. The regression results incorporating these moderating variables are presented in M4 and M6 in Table 3. Additionally, M7 tests the joint moderating effect of both the clustering coefficient and relationship strength.
From the results of M4, it is evident that after including the clustering coefficient as a moderating variable, the regression coefficient of the interaction term between the network intermediary and clustering coefficient is -0.005. This coefficient is significantly negative at the 1% level of significance, validating hypothesis H2.
Similarly, the results of Model M6 show that relationship strength plays a positive moderating role between intermediary centrality and collaborative innovation performance. The regression coefficient is 0.0001 and is statistically significant at the 1% level, thus validating hypothesis H3. This also indicates that the moderating effect of relationship strength is not as strong as that of the clustering coefficient, because its coefficient is close to 0. However, the high significance of its result suggests that when the collaboration intensity of businesses is high, enterprises occupying intermediary positions are more likely to achieve a high level of collaborative innovation performance. Figures 2 and 3 present line charts depicting the moderating effects of the clustering coefficient and relationship strength, respectively. While relationship strength does not exhibit a moderating effect as pronounced as the clustering coefficient, it still exerts a positive moderating effect on the relationship between network intermediaries and collaborative innovation, as indicated by its positive coefficient.
Figure 2. The moderating effect of clustering coefficient. |
Figure 3. The moderating effect of relationship strength. |
4.3 Robustness test
To further examine the robustness of the regression results, two additional methods are employed: first, the original sample is regressed using Poisson regression (PR) and zero-inflated negative binomial regression models (ZNBR) separately; second, the measurement of the core independent variable, network centrality, is replaced with the degree centrality of network nodes as a proxy variable for network centrality. The specific regression analysis results are presented in Table 5.
Table 5. Robustness test results. |
| Variable | M8 | M9 | M10 | M11 | M12 | M13 | M14 |
|---|---|---|---|---|---|---|---|
| PR | ZNBR | PR | PR | ZNBR | ZNBR | NBR | |
| BC | -0.001*** | 0.001*** | 0.000*** | -0.000*** | 0.004*** | 0.002*** | 0.298*** |
| (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | |
| ST | 0.010*** | 0.069*** | 0.0665*** | ||||
| (0.000) | (0.000) | (0.000) | |||||
| BC×ST | 0.000*** | 0.000*** | 1.020e-3*** | ||||
| (0.000) | (0.000) | (0.000) | |||||
| CL | 0.309*** | 0. 208*** | -0.510*** | ||||
| (0.000) | (0.000) | (0.000) | |||||
| BC×CL | -0.002*** | -0.005*** | 0.297*** | ||||
| (0.000) | (0.006) | (0.000) | |||||
| TR | 0.031*** | 0.061*** | 0.030*** | 0.030*** | 0.051*** | 0.058*** | -0.062*** |
| (0.000) | (0.002) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | |
| EC | 0.302*** | -0.011 | 0.360*** | 0.306*** | 0.116*** | -0.0151 | 0.033** |
| (0.000) | (0.024) | (0.000) | (0.000) | (0.000) | (0.536) | (0.037) | |
| CC | 2.158*** | 1.099*** | 2.617*** | 2.361*** | 0.932*** | 1.106*** | 0.497*** |
| (0.000) | (0.140) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | |
| Constant | 0.757*** | 1.887*** | 0.073*** | 0.482*** | 0.492*** | 1.830*** | 0.348*** |
| (0.000) | (0.146) | (0.001) | (0.000) | (0.000) | (0.000) | (0.000) | |
| N | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 | 5,720 |
M8 and M9 represent the regressions using only the core explanatory and control variables with Poisson regression and zero-inflated negative binomial regression, respectively. M10 and M12 involve testing the interaction effect of relationship strength using two regression methods. The results consistently demonstrate that the relationship between network centrality and collaborative innovation performance is negatively moderated by the strength of collaborative relationships, thus confirming the negative moderation hypothesis. M11 and M13 test the interaction effect of the network clustering coefficient using the two regression methods, and similarly reveal that the relationship between network centrality and collaborative innovation performance is negatively moderated by the network clustering coefficient. Finally, M14 replaces the core explanatory variable network centrality with relative betweenness centrality and conducts negative binomial regression (NBR), yielding robust results. Consequently, the core hypotheses of this study exhibit robustness, as confirmed by these robustness checks.
5 Conclusions and discussion
5.1 Conclusions
Based on patent application data spanning from 2006 to 2020, this study explores the roles of network intermediaries, the network clustering coefficient, and the strength of collaborative relationships in shaping firms’ collaborative innovation performance. The findings shed light on the dynamics of collaborative behaviors within innovation networks and offer valuable insights for strategic decision-making.
This study reveals several key conclusions. First, the presence of network intermediaries positively affects collaborative innovation performance. Firms that occupy intermediary positions in the collaboration network serve as bridges for knowledge and technology exchange, thus enhancing the innovation performance of their partners. This observation aligns with social capital theory and underscores the pivotal role of network intermediaries in fostering innovation within organizations. The results suggest that firms leveraging their intermediary positions not only improve their own innovation outcomes but also enhance the overall collaborative potential of the network, contributing to a more vibrant innovation ecosystem.
Second, the network clustering coefficient exerts a negative moderating effect on the relationship between network intermediaries and collaborative innovation performance. While a higher clustering coefficient facilitates knowledge diffusion, an excessive value can lead to redundancy in network information, ultimately reducing opportunities for collaborative innovation. This finding emphasizes the need for balanced network structures because excessive clustering may trap firms within a limited pool of ideas and perspectives, thereby hindering creative breakthroughs. This observation aligns with previous studies (Wang et al., 2019) that highlight the intricate relationship between network structures and innovation dynamics. Woods et al. (2022) also noted that, particularly in the context of low-technology clusters, a firm’s position can influence product development activities. The negative moderating effect of the clustering coefficient could be explained by the interconnected nature of collaborative relationships; as firms rely on central enterprises for resources, individual connections may become diluted. This redundancy often leads to a situation in which firms prioritize their immediate network ties over exploring novel collaborations, resulting in diminished innovation outcomes. In this context, the bridge relationships of network intermediaries conflict with network closure, highlighting the need for management wisdom to achieve balance.
Furthermore, this study highlights that the strength of collaborative relationships positively moderates the relationship between network intermediaries and collaborative innovation performance. Increasing relationship strength enhances the effectiveness of network intermediaries in boosting innovation outcomes. Strong ties contribute to a higher level of trust and reduced uncertainty among partners, fostering an environment conducive to sharing sensitive information and engaging in riskier joint innovative endeavors. This dynamic ultimately drives better innovation performance. The findings suggest that network intermediaries with robust collaborative relationships are better positioned to influence the flow of resources, ideas, and knowledge within a network. This amplifies their intermediary role in enhancing collaborative innovation outcomes. This observation is particularly relevant for organizations seeking to optimize their collaborative strategies as it underscores the importance of nurturing strong ties within their networks.
Compared to previous literature, this research offers new insights into the dual role of network intermediaries and the implications of network structure on innovation. Although existing studies have acknowledged the importance of intermediaries, few have examined the nuanced effects of clustering and relationship strength in collaborative innovation. This study not only identifies the positive role of network intermediaries in enhancing innovation performance, but also highlights the complex interplay between network relationships and network structure. Specifically, it reveals how excessive clustering can hinder innovation by limiting exposure to diverse ideas, whereas strong collaborative ties can amplify the effectiveness of intermediaries. By integrating these dimensions, this research provides a more comprehensive understanding of how network dynamics influence innovation outcomes, addressing a critical gap in the literature. Furthermore, it contributes to the theoretical discourse by proposing a framework that illustrates the delicate balance firms must maintain between leveraging their intermediary positions and fostering strong yet diverse collaborative relationships. This novel perspective not only advances academic understanding but also offers practical implications for firms aiming to optimize their innovation strategies in increasingly complex network environments.
5.2 Managerial implications
The findings of this research have significant managerial implications for industrial enterprises seeking to enhance their collaborative innovation performance. These implications offer guidance for decision-makers in fostering effective collaboration and leveraging network dynamics to achieve innovation goals.
First, leveraging network intermediaries. To fully harness the potential of network intermediaries, firms must strategically identify and engage with pivotal entities within their innovation ecosystems. Intermediaries play a crucial role in bridging the gaps between diverse partners, facilitating knowledge transfer, and enhancing collaborative innovation outcomes. By leveraging their positions, firms can access a wider array of resources and expertise that might otherwise be unavailable, fostering a more comprehensive approach to innovation. Furthermore, firms must recognize that intermediaries can vary in their capabilities and influence. Thus, organizations should assess the competencies of potential intermediaries to ensure alignment with their innovation objectives. This strategic approach enables firms to not only optimize their collaborative efforts but also adapt swiftly to the changing landscape of innovation, thereby maintaining a competitive edge in their respective markets.
Second, strengthening collaborative relationships. To enhance collaborative innovation performance, organizations should prioritize building strong and enduring relationships with their network partners. This involves trust building and mutual learning. Transparent communication and fulfilling commitments foster a strong foundation for collaborative efforts. Co-creating platforms for sharing experiences, challenges, and best practices, leading to a richer exchange of ideas. Especially in China, the strength of collaborative ties is crucial in influencing the relationship between innovation and intermediaries. Strong links can significantly enhance collaborative innovation performance by facilitating trust and resource sharing. In China, where government policies often prioritize manusc industries, these robust ties may enable firms to navigate regulatory landscapes more effectively, thereby fostering innovation. Moreover, the interplay of cultural factors, such as a preference for long-term relationships, can further amplify the positive impact of strong ties on innovation outcomes. While the dynamics of these relationships are observable in other countries, the distinct institutional context in China makes the strength of collaborative ties particularly pivotal for leveraging intermediaries in innovation.
Third, balancing network structures. Firms must find a balance in their network structures to avoid the pitfalls of excessive clustering. While strong ties provide significant benefits, over-reliance on close-knit relationships can lead to information redundancy, which may stifle creativity and innovation. Organizations should actively seek diverse partnerships beyond their immediate network to enhance their innovative capabilities and broaden their access to new ideas, technologies, and markets. This diversity is crucial for fostering a dynamic innovation ecosystem. Moreover, firms should be mindful of the potential for homogeneity within highly clustered networks, as this can limit their exposure to novel perspectives and reduce their ability to adapt to changing market conditions. To counteract these challenges, organizations can implement strategies such as participating in cross-industry collaborations or engaging with international partners to introduce fresh ideas and practices into their innovation processes.
5.3 Limitations and further research
This study has several limitations that provide avenues for future research. First, while our findings offer insights into the relationship between network intermediaries and innovation in China, they are largely based on quantitative data derived from social network analysis. Future research could employ qualitative methods such as interviews and case studies to capture the subjective experiences of firms and intermediaries. This could enrich our understanding of how institutional contexts and cultural factors influence collaborative behavior and innovation outcomes. Second, our research primarily focuses on China, and while the findings may have implications for other contexts, cross-country comparisons are warranted. Future studies could investigate whether the dynamics identified here are consistent across countries with varying levels of government intervention in innovation.
Funding information
This work was supported by the National Social Science Fund of China (No. 22FGLB035), and Fujian Provincial Federation of Social Sciences (No. FJ2023B109).
Author contributions
Zhiwei Zhang (zw-zhang@cueb.edu.cn, ORCID: 0009-0002-3100-2407): Formal analysis (Lead), Writing - original draft (Lead).
Wenhao Zhou (wenhaoz2021@stu.hqu.edu.cn, ORCID: 0000-0001-9421-8526): Conceptualization (Lead), Methodology (Lead).
Data availability statement
The authors declare that the data in this paper will be made available upon reasonable request.