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Regional innovation networks, as a significant component of the national innovation systems, play a crucial role in promoting economic development. Classical works in the field of innovation networks, emphasizing satisfactory performance among innovators, underscore the importance of a dense network structure with small-world properties (Gay & Dousset, 2005). This topology, quantified by the average shortest distance, increases the probability of collaboration between groups of innovators (Amaral et al., 2000; Caloghirou et al., 2021). However, collaboration within these networks often introduces competitive issues such as income inequality, moral hazard, information asymmetry, and technical barriers (Uzzi & Spiro, 2005). Consequently, the links between stakeholders in partnerships are unstable (Bassett et al., 2014). These dynamic structural changes offer new insights for studying the functionality of innovation networks (Fleming et al., 2007).
Increased interest in the relationship between connection patterns and the function of innovation networks has led to various new developments in both empirical and analytical studies (Schilling & Phelps, 2007; Phelps, 2010; Zhang et al., 2016; Bertotti et al., 2016; Casablanca et al., 2023). However, the literature has primarily focused on a single network-based view, limited to exploring interactions among various innovators, such as scientists and their teams, enterprise technicians and engineers, universities and research institutes, and government departments. With a growing emphasis on the resilience and function of networks, there is an urgent need to broaden our understanding of strong interfirm networks with dynamic partnerships, taking a new perspective on structural heterogeneity, which determines the endogenous architecture of the network (Briscoe & Rogan, 2016; Bernard et al., 2022). Consequently, scholars are increasingly shifting their research perspectives toward the diversity of connections and network functions across multiple networks, as evidenced by recent research (Peres, 2014; Li & Zhang, 2015; Bin & Sun, 2022).
The structural heterogeneity of regional innovation networks reflects the dynamic linking process, directly influenced by innovators' behavior and innovative uncertainty (Mazzola et al., 2015). Factors such as knowledge spillover and research and development (R&D) collaboration may increase links within the innovation networks, while credit risk, technical failure, and partnership failure may decrease them (Gay & Dousset, 2005; Wu & Wu, 2014; Vivona et al., 2023). Drawing from the network embeddedness perspective, each innovator should optimize the technological distance between partners and secure a strategic position within the alliance network to absorb knowledge and information from external sources (Phelps, 2010; Han et al., 2020). Trust, influenced by changes in network configuration, plays a dominant role in establishing strong links (Shazi et al., 2015). Additionally, the absorptive capacity of external knowledge also has positive impacts on innovative partnerships and the overall network density (Tortoriello, 2015).
The utilization of generating functions with connected probability allows for the exploration of the structural heterogeneity of regional innovation networks, providing insights into the process of randomly choosing partners among innovators (Li & Zhang, 2015). The percolation threshold of the giant linked group varies significantly based on probability (Morone & Makse, 2015; Ziff et al., 2020). This threshold holds crucial importance in setting policies aimed at achieving the highest performance to facilitate the spread of technology within regional innovation networks (Zhao et al., 2023; Tabassum et al., 2022).