Abstract
Regional economic resilience has become a central topic in economic geography, particularly concerning the dynamics of regional development. A resilient industrial system is crucial for economic stability; thus, enhancing industrial resilience is vital for promoting high-quality regional economic growth. This study utilizes invention patent authorization data and industrial enterprise data from 41 cities in the Yangtze River Delta between 2005 and 2020 to quantitatively assess regional industrial resilience and the technological network structures. Through panel regression analysis, the study explores the mechanisms by which technological network structures influence regional industrial resilience, aiming to provide new insights from a technological network perspective. The findings indicate that industrial resilience in the Yangtze River Delta generally exhibits an upward trend followed by a decline, with significant spatial disparities. Shanghai maintains a relatively high level of industrial resilience. The robustness of technological network has increased over time under both random and targeted node removal scenarios, with Shanghai consistently demonstrating the highest network robustness. Cities such as Nanjing, Hangzhou, Hefei, and Suzhou also show rapid growth. Regression analysis reveals that technological network robustness has a significant positive impact on regional industrial resilience, with the strength of this impact intensifying as the proportion of targeted node removal increases. Moreover, technological related variety negatively affects industrial resilience, whereas unrelated variety has a significant positive effect. However, the influence of technological relatedness is notably weaker than that of network robustness.
Keywords:
Technological Network Structure
Industrial Resilience
Technological Network Robustness
Yangtze River Delta
A
1 Introduction
The accelerated evolution of global uncertainties—driven by events such as the U.S.-China trade frictions, the COVID-19 pandemic, and the Russia-Ukraine conflict—has placed mounting pressures on China’s economic system. These disruptions highlight the increasing frequency and intensity of external shocks. As emphasized in the report of the 20th National Congress of the Communist Party of China, the country has entered a period characterized by both strategic opportunities and growing, unpredictable risks. This context underscores the urgent need to strengthen research on adaptive restructuring of regional economies under uncertainty—an emerging focus in the field of economic geography. Resilience, as a concept, captures a system’s ability to withstand, absorb, and adapt to crises and disruptions. In recent years, regional economic resilience has become a central topic in economic geography, providing critical insights into the dynamics of regional development. Drawing on evolutionary thinking, scholars define regional economic resilience as the ability of a regional economy to resist external shocks, recover to its previous growth path, restructure its economic base, and even chart new development trajectories (Martin, 2012; Li et al., 2019; Martin & Sunley, 2015). This framework offers important theoretical foundations and methodological tools for understanding how China can respond to crises and achieve high-quality economic development.
Scholars have conducted sustained research on the concept, analytical frameworks, measurement methods, and influencing factors of regional economic resilience, with a growing diversity of approaches and findings (Tian et al., 2023). Building upon this understanding, the scale of analysis has become increasingly refined, prompting scholars to explore resilience characteristics across different industries, such as industrial resilience and tourism resilience (Hu et al., 2021; Di et al., 2023). As a core pillar of regional development, the industrial sector plays a critical role in stabilizing economic growth (Research Group of the Institute of Industrial Economics, Chinese Academy of Social Sciences, 2022). A resilient industrial system is therefore seen as a key lever for economic stability. Accordingly, scholars have begun to examine how regional industrial systems respond to various disruptions across different spatial scales, analyzing the factors, mechanisms, and pathways that influence improvements in industrial resilience (Lu et al., 2021; Hu et al., 2021; Guan et al., 2021). Empirical studies on regional industrial resilience commonly employ key indicators such as industrial output, employment rates, and firm survival rates, drawing on both macroeconomic and micro-level enterprise data. These studies frequently investigate structural determinants—such as industrial diversification, specialization, and technological variety—to understand the formation of industrial resilience. However, current research faces two key limitations. First, existing measurements of industrial resilience tend to focus primarily on resistance and recovery at the macro level, often neglecting the dimension of reorientation or transformation. Second, structural characteristics are typically assessed based on pre-defined industrial classifications, such as those established by international standard industry codes. This approach may fail to accurately capture the nuanced features of regional economic structures, thereby limiting explanatory power and policy insights.
In recent years, with the maturation of network science methodologies and the rapid advancement of big data technologies, new theoretical frameworks and technical support have emerged to address the limitations of traditional research perspectives. The network perspective enables the capture of regional economic structural characteristics across multiple spatial scales and reveals the interrelationships among different industries, technologies, and knowledge domains, as well as their evolutionary trends over time (Fratesi et al., 2016). Meanwhile, enterprises, as the fundamental units of regional economic activities, not only serve as the micro-level carriers of industrial structural evolution but also act as the primary drivers of regional industrial restructuring. Enterprises undergo dynamic processes of entry, growth, decline, transformation, and exit in the market, reflecting the micro-level manifestations and formation mechanisms of regional industrial resilience (Tan et al., 2023). Therefore, from the viewpoint of network science, exploring the unified mechanisms through which regional technological network structures influence micro-level industrial resilience—its pathways and intrinsic mechanisms—can provide theoretical foundations and policy insights for the high-quality development of regional economies.
Based on this, the study takes the Yangtze River Delta, a typical export-oriented economic region, as a case to construct regional technological networks and measure their structural indicators in order to accurately characterize regional economic structural features. At the same time, using micro-level enterprise data, it develops industrial resilience metrics across three dimensions—resistance, recovery, and reconfiguration—to systematically analyze the influence of regional technological network structures on industrial resilience.
The remainder of the paper is structured as follows. The next section presents the literature review and hypotheses. Then we describe the data, variables and econometric model. The fourth and fifth section discusses the main findings and results. The final section concludes the paper.
2 Literature Review and Research Hypotheses
Since the global financial crisis, regional economic resilience has gradually become a focal topic in academic research. Building upon quantitative measurements of regional economic resilience, an increasing number of studies have turned their attention to its underlying formation mechanisms. Martin (2015) was among the early scholars to propose a framework analyzing the influencing factors of regional economic resilience, highlighting that multidimensional factors—such as economic structure, labor force, financial capital, and institutional policies—jointly shape regional resilience. This study focuses specifically on regional economic structure, with particular emphasis on technology, widely regarded as the primary productive force. The aim is to explore, from the perspective of network science, the mechanisms through which regional technological network structures influence industrial resilience. As a core component of regional economic resilience, industrial resilience reflects the industrial system’s capabilities to resist, recover from, and reconfigure in response to external shocks. Its evolutionary characteristics largely determine the overall resilience level of the regional economy. However, existing studies have primarily focused on the impact of technological structure on regional economic resilience, with limited systematic and in-depth exploration of its role in the formation of industrial resilience. Compared to macro-level economic resilience, the influence of technological structure on industrial resilience is more direct and tangible. Nevertheless, most current research continues to emphasize the effects of technological structure on regional economic resilience, leaving the mechanisms through which it shapes industrial resilience largely underexplored. To address this gap, the present study draws on relevant research and seeks to extend the theoretical framework linking technological structure and regional economic resilience to the context of industrial resilience. Specifically, it systematically investigates how the structural characteristics of regional technological networks contribute to the formation and evolution of industrial resilience.
2.1 Technological (Un) Related Variety and Regional Industrial Resilience
In the field of economic geography, regional economic structure has become one of the core starting points for research on regional economic resilience. Early studies primarily focused on the differences in how two types of regional economic structures—specialization and diversification—affect resilience, with particular attention given to the impacts of industrial specialization and diversification (Boschma, 2017). However, the essence of industrial structure lies in technological structure; industrial configurations are the result of different combinations of technologies. Thus, the diversification and specialization of technology form the underlying logic of industrial and economic development (Teng et al., 2023; Balland et al., 2015). Scholars generally agree that regions with a high degree of technological specialization tend to exhibit lower levels of resilience when confronted with shocks, whereas regions with more diversified technological structures tend to display stronger resilience (Teng et al., 2023; Guo et al., 2018). This is because, when disruptions occur, a technologically diversified structure can spread the shock across different technological domains, thereby reducing its concentrated impact on any single sector and increasing the likelihood that each technological domain can recover (Balland et al., 2015; Brakman et al., 2015). However, excessive technological diversification may lead to a lack of connectivity between regional technologies, hindering the generation of innovation and the diffusion of positive externalities, which in turn could undermine the long-term development potential of the regional economy (Rocchetta et al., 2022). As a result, the mechanisms through which technological diversification affects regional resilience remain a matter of academic debate.
To address the limitations of the traditional concept of diversity, Frenken et al. (2007) proposed a distinction between related variety and unrelated variety within diversified regional economic structures, thereby enabling more nuanced analyses of how different types of variety influence regional economic resilience. As Frenken’s original work applied these concepts at the industrial level, subsequent scholars have largely followed this approach, employing industrial statistical data to measure related and unrelated variety and examining their respective impacts on regional economic resilience (Tan et al., 2020). More recently, this framework has been extended to the technological domain. Scholars have begun to use patent data to assess related and unrelated technological variety and analyze their effects on regional economic resilience (Tóth et al., 2022; Rocchetta et al., 2022; Chen et al., 2024). Related technological variety refers to a regional portfolio of technologies that are significantly interrelated or complementary. It emphasizes the spatial co-location of related but distinct technologies, and its mechanism operates through Jacobs’s externalities to enhance the recoverability of the regional economy in the face of shocks. Specifically, related variety reduces cognitive distance between technologies, facilitates knowledge exchange and spillovers, and promotes innovation efficiency, thereby increasing the likelihood of new industries and technologies emerging in the region, which in turn strengthens regional economic recovery (Tóth et al., 2022; Chen et al., 2025). Additionally, when a region encounters external disruptions, technologically related industries can leverage their similarities to reorganize resources and pursue mergers and restructuring, fostering industrial upgrading and facilitating rapid economic recovery (Chen, 2022). Unrelated technological variety emphasizes the low degree of interconnection among a region’s technological resources—that is, the coexistence of multiple, distinct, and unrelated technological domains. Its underlying mechanism operates through portfolio effects, which enhance a region’s economic resistance to external shocks. Specifically, when facing asymmetric shocks, a region characterized by unrelated technological variety can effectively disperse the disruptive impact across different technological sectors, thereby preventing the further spread of risk. At its core, this mechanism strengthens the region’s capacity to withstand external disturbances (Tóth et al., 2022; Boschma, 2017). Based on the above, this study proposes the following hypotheses:
2.2 Technological Network Structure and Regional Industrial Resilience
Although related and unrelated variety can to some extent capture the structural characteristics of regional economies, the criteria used to determine whether technologies are “related” or “unrelated” are often based on international industrial classification systems or other technical taxonomies, rather than actual linkages among industries or technologies. In response, recent studies have begun to explore regional economic resilience based on empirically grounded representations of regional economic structures (Tóth et al., 2022; Rocchetta et al., 2022). At present, the network perspective has become a key analytical approach in economic geography for examining the real structure of regional economies. In fact, as early as 2007, Martin and Sunley emphasized the need to further develop a network-based perspective within the field of economic geography. However, due to limitations in data availability and methodological tools, the network approach did not initially gain widespread traction in the discipline.
With the maturation of network science—particularly methodologies derived from the product space—and the rise of big data, scholars have increasingly adopted a network perspective to study regional economic development. Concepts such as regional technological networks (Tóth et al., 2022), regional knowledge networks (Ye et al., 2024), and regional innovation networks (Cao et al., 2023) have been proposed to capture the structural dynamics of regional economies. Among them, regional technological and knowledge networks refer to networks composed of different technological and knowledge domains involved in regional innovation activities. These two are often used interchangeably in empirical research, as both rely on patent and publication data as proxies (Ye et al., 2024). In contrast, regional innovation networks focus on the network of various stakeholders engaged in regional innovation. Drawing on established literature (Tóth et al., 2022; Ye et al., 2024; Cao et al., 2023), this study adopts the concept of the regional technological network to represent the structure of the regional economy, based on the premise that the recombination of different technological domains is a direct driver of regional innovation and economic development. In a regional technological network, nodes represent technological domains, and edges reflect the connections and combinations between them. These diverse combinations enable various forms of economic innovation. While existing research has primarily examined how the structure of regional technological networks influences the emergence of new technologies and regional innovation performance, their impact on regional economic resilience remains underexplored—and their influence on industrial resilience has received even less scholarly attention (Du et al., 2022).
From a network-based perspective, regional technological networks exhibit varying levels of robustness depending on their structural configurations. These differences in robustness can, in turn, lead to divergent levels of economic resilience when regions face external shocks. First, network robustness refers to a network’s ability to continue functioning despite the loss of certain nodes or connections (Albert et al., 2000; Solé et al., 2008). In network science, assessing whether a network can maintain its core functionality typically involves examining the presence of a giant component—a connected subgraph that encompasses a substantial portion of all nodes in the network. Generally, for any given network structure, a giant component will persist and support network functionality as long as node removal remains below a certain threshold. However, once the degree of node failure exceeds this threshold, the network tends to fragment into disconnected subgraphs, ultimately leading to systemic collapse (Zitnik et al., 2019). Moreover, not only the number of nodes removed but also the attributes of the removed nodes critically influence network robustness. Specifically, targeted removal of high-degree nodes (i.e., nodes with numerous connections) tends to degrade network robustness more severely than random node removal (Tóth et al., 2022). For example, in a star-shaped regional technological network—where one central node connects multiple peripheral nodes—removing the central node disrupts the entire network structure, splitting it into isolated components. In contrast, random removal is more likely to affect peripheral nodes, allowing the network to maintain connectivity through the central hub. Second, the robustness of a regional technological network plays a crucial role in shaping the resilience of regional economies through its influence on resistance, recovery, and reconfiguration. On one hand, networks with high robustness demonstrate stronger resistance to shocks, as they are more likely to preserve their giant components when subjected to node loss. This structural stability allows economic activities to continue largely undisturbed during crises. On the other hand, such networks also facilitate recovery and reconfiguration, since their high degree of connectivity provides multiple pathways for technological recombination and innovation. This, in turn, promotes the emergence of new technologies and revitalizes regional economic activity, enabling the exploration of novel development trajectories (Tóth et al., 2022). In summary, we propose the following hypothesis:
3. Research Methodology and Data Sources
3.1 Research Methodology
(1) Measurement of Industrial Resilience
Following the analytical framework proposed by Martin et al. (2015), this study conceptualizes industrial resilience along three temporal and process-based dimensions: resistance, recovery, and reconfiguration.
First, reconfiguration captures the processes of reorientation and renewal following external shocks. Drawing on existing literature, this study measures regional resistance using the firm survival rate, which reflects the ability of a regional industrial system to withstand external disruptions without substantial firm exits. Specifically, firms with statuses such as “active” or “in operation” are classified as surviving firms, while those marked as “deregistered,” “revoked,” or “relocated” are considered exiting firms. The survival rate is calculated as follows:
In the formula,
and
represent the number of surviving and exiting firms, respectively, in region
c during year
i. While
denotes the firm survival rate of region
c in year
i.
Second, regional recovery is measured by the firm entry rate, which captures the ability of the industrial system to regenerate economic activity following a shock. The entry rate is calculated as follows:
In the formula,
represents the number of surviving firms in region
c at the end of year
i, and
represents the number of surviving firms in region
c at the end of year
i − 1.
Third, this study uses two indicators—industrial diversification index (VAR) and industrial upgrading index (UPG)—to capture the reconfiguration dimension of industrial resilience. The industrial diversification index is calculated using an entropy-based method, as expressed in the following formula:
In the formula,
n denotes the number of industry categories, and
represents the proportion of firms in a given industry within region
c in year
i.
Finally, for industrial upgrading index, industrial firms are classified into three categories—labor-intensive, resource-intensive, and technology-intensive. An improved structural similarity coefficient method is employed to measure the degree of industrial structural upgrading. First, the proportion of each type of industrial firm (labor-intensive, resource-intensive, and technology-intensive) in the total number of firms is treated as a component of a spatial vector, forming a three-dimensional vector
=(
,
,
). Second, the angles
、
、
between
and the reference vectors representing ascending levels of industrial sophistication—
=(1, 0, 0),
=(0, 1, 0),
=(0, 0, 1)—are calculated, respectively.
The calculation formula for the Industrial Upgrading Index is as follows:
(2) Related and Unrelated Technological Variety
This study follows the entropy-based approach proposed by relevant scholars to construct indicators for cities’ related and unrelated technological variety (Fratesi et al., 2016; Tóth et al.,
2022). According to the entropy decomposition formula by Theil, Unrelated Variety (UV) measures the entropy between groups (i.e., at the one-digit patent classification level), while Related Variety (RV) captures the entropy within groups (i.e., at the three-digit patent classification level). Specifically, the calculation formulas for unrelated and related variety are as follows:
In the formula,
represents the proportion of one-digit patent category
in city
r relative to all patents in that city, while
denotes the proportion of three-digit patent iii within the one-digit category
in city
r.
(3) Technical Network Robustness
This study calculates the robustness of technological network in two main steps. First, we construct the city-level technology network or technological space using patent data. The core of this approach lies in assessing the relatedness between pairs of technology nodes. Specifically, we follow the co-occurrence method proposed by Hidalgo et al. (
2007) and Zhang & Rigby (
2022).The fundamental idea is that if two technologies frequently co-occur within the same patent document, it indicates that they likely share a similar knowledge base. Consequently, a high co-occurrence probability suggests a strong technological relatedness between the two. The formula for computing technological relatedness is as follows:
Where
denotes the relatedness between technologies
i and
j;
represents the number of patents that simultaneously contain both technologies
i and
j;
and
are the total number of patents containing technologies
i and
j, respectively.
Based on the calculated relatedness between technologies within a city, a city-level technology network can be constructed. In this network, the nodes represent different categories of patented technologies, and the size of each node reflects the number of patents in that category. The edges between nodes indicate the degree of relatedness between technologies—the higher the relatedness, the shorter the distance between the nodes.
The second step involves assessing the structural robustness of the city’s technology network. The core idea is to measure the proportion of nodes that must be removed to dismantle the network’s giant connected component. This is calculated using the Molloy–Reed criterion. According to this criterion, for a giant component to exist in a network, most of the nodes within it must have at least two neighbors. Specifically, if the K value of a network is greater than 2, a giant connected component exists; if the K value is less than 2, the network lacks a giant component and instead consists of many disconnected components.
Here, k represents the number of edges connected to a given node; 〈k〉 denotes the average k value across the entire network; k² refers to the square of the number of edges connected to a given node; and 〈k²〉 represents the average k² value across all nodes in the network.
Finally, using the Molloy–Reed criterion as the standard, we calculate the proportion of nodes that must be removed for the network’s K value to equal 2. Regarding the node removal methods, there are two types: random removal and targeted removal. Random removal involves randomly sampling and removing nodes from the network, while targeted removal prioritizes removing nodes with higher degrees. Through these two approaches, we ultimately determine the maximum percentage of targeted removal and the maximum percentage of random removal that the city’s technology network can withstand.
3.2 Data Sources
This study measures industrial resilience using data from industrial enterprises. Enterprise information was obtained from the Tianyancha website (https://www.tianyancha.com/). The selected industries include “Mining,” “Electricity, Heat, Gas, and Water Production and Supply,” and “Manufacturing.” The query filtered enterprises with registered capital of over 10 million RMB and institutional type classified as enterprises. The data cover industrial enterprises registered between January 1, 2005, and December 31, 2020, resulting in information on a total of 405,851 industrial enterprises. The data for the technology network come from patent data sourced from the China National Intellectual Property Administration website. Among the patent types in China—invention patents, utility models, and design patents—this study focuses on invention patents due to their higher technological content. The dataset includes a total of approximately 3.8146 million invention patent records from 2005 to 2020.
3.3 Study Area
According to the "Yangtze River Delta Regional Integrated Development Plan Outline" approved by the State Council in 2019, the Yangtze River Delta (YRD) includes the entirety of Shanghai Municipality, Jiangsu, Zhejiang, and Anhui provinces, comprising a total of 41 prefecture-level and above cities. In 2023, the combined GDP of the three provinces and one municipality reached approximately 30.5 trillion yuan, accounting for nearly one-quarter of the national economic output. The region also recorded 819,200 granted invention patents in 2023, representing 30.21% of the total patents granted nationwide. Overall, the Yangtze River Delta is one of China’s most economically dynamic regions, boasting the strongest technological innovation capacity and the highest degree of openness to the outside world, playing a key role as the stabilizing force of China’s economy.
4 Industrial Resilience and Technological Network Structure in the Yangtze River Delta
4.1 Characteristics of Industrial Resilience
This study calculates the industrial resilience scores for 41 prefecture-level cities in the YRD from 2005 to 2020. To ensure comparability across cities, the results are standardized using the Z-score method. Spatial visualizations of industrial resilience for four benchmark years—2005, 2010, 2015, and 2020—are presented in Fig. 1. The following key findings emerge: First, industrial resilience in the YRD shows a general trend of rising initially and then declining. The mean resilience scores for the four selected years are 0.386 (2005), 0.606 (2010), 0.374 (2015), and − 0.986 (2020). The significant increase in 2010 suggests that the YRD demonstrated strong industrial resilience in the 2008 global financial crisis. In contrast, the sharp decline in 2020 can be largely attributed to the accelerated exit of industrial firms under the impact of the COVID-19 pandemic. Second, regional disparities in industrial resilience across the YRD initially narrowed but later widened. The standard deviation of resilience scores for the four years are 1.713 (2005), 1.344 (2010), 1.342 (2015), and 1.926 (2020), indicating that disparity decreased after the global financial crisis but increased again during the pandemic. Third, a clear pattern of inter-provincial variation in industrial resilience emerges. Shanghai consistently exhibits higher levels of resilience, followed by Jiangsu, Anhui, and Zhejiang in 2015 and 2020. Notably, in 2010, Anhui outperformed Jiangsu in terms of industrial resilience, possibly reflecting the effects of targeted regional development policies. Fourth, in terms of spatial clustering, the high-resilience cities in the YRD do not exhibit a strong and consistent spatial concentration pattern over the years. However, certain years—particularly 2010 and 2015—do show visible clusters of high resilience in northern Jiangsu and northern Anhui. These findings highlight the temporal dynamics and spatial heterogeneity of industrial resilience in the YRD and underscore the need to consider both firm-level and regional structural factors in resilience-building strategies.
4.2 Characteristics of Technological Networks Structure
To assess the robustness of technological networks across the YRD, we compute network robustness under two scenarios—random removal and targeted removal—for four benchmark years. The results are illustrated in Figs. 2 and 3. A spatial analysis of the technological network robustness in the YRD reveals several key insights (Fig. 2): First, technological networks are significantly more robust under random removal than under targeted removal. In 2020, the average robustness threshold for targeted removal across the 41 cities in the YRD was 2.9%, compared to 25% under random removal. This indicates that removing just the top 2.9% of highest-degree nodes causes the network to lose its giant connected component and collapse, whereas a network can endure random removal of up to 25% of its nodes before disintegration. Second, under targeted removal, cities such as Shanghai, Hangzhou, Suzhou, and Nanjing exhibit relatively high levels of network robustness. Under random removal, the high-robustness cities include Shanghai, Hangzhou, Nanjing, Suzhou, and Hefei. Overall, whether under random or targeted node removal, municipalities directly under central government jurisdiction (Shanghai), provincial capitals (Nanjing, Hangzhou, Hefei), and economically advanced cities (Suzhou) demonstrate stronger technological network robustness. However, Hefei’s lower robustness under targeted removal highlights its vulnerability to disruptions at critical technological nodes, suggesting an insufficient capacity to address potential “chokepoints” in key technology areas.
Figure 3 presents the distribution characteristics of technological network robustness in the YRD for the years 2005, 2010, and 2015. Several key patterns emerge: In 2005, under both random and targeted removal scenarios, only Shanghai exhibited high robustness, while most other cities were categorized as low-value regions. This suggests that, aside from Shanghai, the technological networks in the YRD were generally at a low and evenly distributed development stage, characterized by low node degrees and weak connectivity, resulting in limited network robustness. By 2010, Shanghai remained the only city in the high-value category across both removal scenarios. However, mid-high value cities such as Nanjing, Hangzhou, and Suzhou began to emerge, especially under random removal, where their network robustness saw significant improvement. This indicates the beginning of a more differentiated and hierarchical regional technological network structure. In 2015, under targeted removal, Shanghai, Suzhou, and Nanjing entered the high-robustness category, while Hefei, Wuxi, Hangzhou, Zhenjiang, Fuyang, and Wenzhou developed into mid-high value regions. Under random removal, Shanghai and Suzhou remained highly robust, while Wuxi, Nanjing, Hefei, Hangzhou, and Wuhu were classified as mid-high value regions. These changes reflect a significant enhancement in technological network robustness across YRD cities during this period. Overall, both under random and targeted removal, the robustness of technological networks in the YRD increased steadily over time. Robustness was consistently higher under random removal than under targeted removal. Shanghai maintained its position as the most robust city throughout the period, while Nanjing, Suzhou, Hangzhou, and Hefei—as provincial capitals or regional economic hubs—experienced rapid growth in network robustness.
To further examine the long-term dynamics of technological network robustness, Fig. 4 presents the tolerance levels of four representative cities—Shanghai, Nanjing, Hangzhou, and Hefei—to targeted and random removal from 2005 to 2020. In the figure, the green line represents targeted removal, the yellow line indicates random removal, and the red dashed line marks the critical threshold (K = 2) at which the giant component collapses. The intersection of the green line and the red line represents the maximum proportion of targeted removal a city's technological network can tolerate before structural collapse, while the intersection of the yellow line and the red line denotes the maximum tolerance to random removal. The results show that Shanghai demonstrates the highest robustness, withstanding up to 27% targeted removal and 89% random removal, significantly outperforming the other cities. Nanjing, Hangzhou, and Hefei show targeted removal tolerances of 20%, 20%, and 15%, respectively, and random removal tolerances of 84%, 82%, and 81%. These findings reinforce that, over a long temporal scale, Shanghai consistently exhibits the most robust technological network in the YRD. Notably, its robustness under targeted node attacks far surpasses that of the other cities. While Nanjing and Hangzhou show relatively strong performance under random attacks, their networks remain vulnerable to targeted attacks. Hefei, in particular, displays limited robustness under targeted removal.
5. The Impact of Technological Network Structure on Regional Economic Resilience
5.1 Model Construction and Variable Description
This study employs regional industrial resilience as the dependent variable, while the explanatory variables include: technological network robustness, related variety (RV), unrelated variety (UV). Technological network robustness is captured using six indicators, namely: the maximum tolerable percentage of targeted node removal (Targeted Removal), the maximum tolerable percentage of random node removal (Random Removal), a series of scenario-based indicators reflecting robustness under varying levels of node removal—specifically: 20% targeted (or 80% random) removal (target_02); 40% targeted removal (target_04); 60% targeted removal (target_06); 80% targeted removal (target_08). To investigate how technological related and unrelated variety, as well as technological network robustness, influence regional industrial resilience, this study constructs a panel ordinary least squares (OLS) regression model. The general form of the model is specified as follows:
In the above equation, the meanings of all variables are as previously defined, and
represents the regression residual.
5.2 Analysis of Regression Results
The regression results of the econometric models are presented in Table 1. Regarding technological network robustness, Model (1), which uses the maximum tolerance for random removal as the key explanatory variable, shows a significantly positive impact on industrial resilience. This indicates that the higher the robustness of a city's technological network, the stronger its industrial resilience—thus confirming Hypothesis 3. Model (6), which employs the maximum tolerance for targeted removal, similarly demonstrates a statistically significant and positive relationship between network robustness and industrial resilience, further validating Hypothesis 3. Across Models (1) through (6), related variety exhibits a significantly negative effect on industrial resilience. In other words, cities with higher levels of related technological variety tend to exhibit lower levels of industrial resilience, thereby failing to support Hypothesis 1. This result suggests that although related variety can facilitate knowledge spillovers among cognitively proximate industries and enhance regional economic dynamism, it may also reduce a system’s ability to withstand external shocks. Specifically in industrial systems—which tend to be more closed and structurally interdependent—high relatedness reinforces technological coupling and path dependency. As a result, risk transmission becomes more efficient, system redundancy is reduced, and overall industrial resilience is weakened. This finding contrasts with previous research that generally associates related variety with greater economic resilience, highlighting the distinct structural characteristics of industrial systems. Conversely, the regression results across all models reveal a significantly positive effect of unrelated variety on industrial resilience, thereby supporting Hypothesis 2. This suggests that a more diversified and unrelated technological structure contributes to enhanced regional industrial resilience by reducing systemic vulnerability. Furthermore, by comparing the regression coefficients in Models (1) and (6), it is evident that the effects of technological variety (both related and unrelated) are weaker than those of technological network robustness (based on both random and targeted node removal). This highlights the analytical advantage of using a network-based robustness metric over traditional variety indicators in assessing regional industrial resilience. (All independent variables were standardized in the regression models, ensuring comparability across coefficients.)
A comparison between Model (1) and Model (6) reveals that the regression coefficient representing technological network robustness under targeted removal (6.677) is significantly greater than that under random removal (1.240). To further explore this difference, Models (2) through (5) incorporate varying proportions of targeted and random removal. The regression results under each removal scenario are statistically significant, and a clear pattern emerges: as the proportion of targeted node removal increases, the corresponding regression coefficient—indicating the impact of technological network robustness on industrial resilience—also increases. These findings suggest that in the process of enhancing industrial resilience through improving technological network robustness, greater attention should be paid to high-degree nodes within the network. Strengthening the robustness of these key nodes can substantially improve the overall stability of the urban technological network, thereby reinforcing regional industrial resilience.
Table 1
Regression Results of Industrial Resilience in the Yangtze River Delta
| | (1) | (2) | (3) | (4) | (5) | (6) |
|---|
Random Removal | 1.240** | | | | | |
(0.513) | | | | | |
target_02 | | 2.585** | | | | |
| | | (1.135) | | | | |
target_04 | | | 3.636** | | | |
| | | | (1.707) | | | |
target_06 | | | | 4.893** | | |
| | | | | (2.244) | | |
target_08 | | | | | 5.935** | |
| | | | | | (2.894) | |
Targeted Removal | | | | | | 6.677** |
| | | | | | (3.396) |
rv | -0.423* | -0.435* | -0.444** | -0.441** | -0.444** | -0.452** |
| | (0.227) | (0.224) | (0.219) | (0.220) | (0.220) | (0.220) |
uv | 0.669** | 0.639** | 0.636* | 0.637* | 0.635* | 0.635* |
| | (0.321) | (0.324) | (0.324) | (0.324) | (0.324) | (0.324) |
_cons | -0.720 | -0.553 | -0.515 | -0.523 | -0.510 | -0.484 |
| | (0.786) | (0.765) | (0.756) | (0.759) | (0.759) | (0.759) |
N | 656 | 656 | 656 | 656 | 656 | 656 |
Log Lik | -955.855 | -956.614 | -956.796 | -956.755 | -956.866 | -957.091 |
r2 | 0.523 | 0.522 | 0.522 | 0.522 | 0.521 | 0.521 |
| Standard errors in parentheses |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
5.3 Robustness Check
This study conducts a robustness check of the baseline regression results by replacing key variables. Considering that regional industrial resilience comprises three dimensions—resistance, recovery, and reconfiguration—we substitute the original dependent variable, regional industrial resilience, with resistance. By replacing the dependent variable with a single-dimension measure, we test the stability and consistency of the regression results (in Table 2). The results show that the regression outcomes using resistance are consistent with those obtained using overall industrial resilience, indicating that the findings are robust.
Table 2
Regression Results of Industrial Resistance in the Yangtze River Delta
| | (1) | (2) | (3) | (4) | (5) | (6) |
|---|
Random Removal | 0.863*** | | | | | |
(-0.313) | | | | | |
target_02 | | 1.511** | | | | |
| | | (-0.715) | | | | |
target_04 | | | 2.031* | | | |
| | | | (-1.158) | | | |
target_06 | | | | 2.886* | | |
| | | | | (-1.485) | | |
target_08 | | | | | 3.403* | |
| | | | | | (-1.915) | |
Targeted Removal | | | | | | 3.817* |
| | | | | | (-2.239) |
rv | -0.299** | -0.324** | -0.332** | -0.326** | -0.331** | -0.335** |
| | (-0.137) | (-0.134) | (-0.129) | (-0.13) | (-0.13) | (-0.13) |
uv | 0.098 | 0.072 | 0.069 | 0.071 | 0.069 | 0.069 |
| | (-0.19) | (-0.192) | (-0.193) | (-0.193) | (-0.193) | (-0.193) |
_cons | 0.446 | 0.628 | 0.665 | 0.643 | 0.66 | 0.675 |
| | (-0.528) | (-0.52) | (-0.512) | (-0.513) | (-0.513) | (-0.513) |
N | 656 | 656 | 656 | 656 | 656 | 656 |
Log Lik | -722.234 | 723.756 | 724.033 | 723.823 | 723.996 | 724.155 |
r2 | 0.47 | 0.467 | 0.467 | 0.467 | 0.467 | 0.467 |
| Standard errors in parentheses |
| * p < 0.1, ** p < 0.05, *** p < 0.01 |
6 Conclusions and Discussion
6.1 Conclusions
Based on invention patent authorization data and industrial enterprise data from 2005 to 2020, this study quantitatively evaluates the industrial resilience and technological network structure of 41 cities in the YRD. It analyzes the spatiotemporal evolution of network robustness under both random and targeted removals, with a particular focus on the tolerance levels of four representative cities—Shanghai, Nanjing, Hangzhou, and Hefei—under different node removal scenarios. Finally, a panel regression model is employed to explore how related/unrelated technological variety and network robustness influence industrial resilience. Drawing from network science, the study offers new insights into regional industrial resilience and reaches the following key conclusions:
(1) With respect to the temporal and spatial evolution of industrial resilience, industrial resilience in the YRD region shows an overall trend of rising and then declining. A significant drop is observed in 2020. Regional disparities in resilience are notable, with Shanghai consistently exhibiting high resilience levels. However, high-value clusters of industrial resilience are not spatially prominent.
(2) Concerning the technology network robustness, technological networks are significantly more robust under random node removals than under targeted ones. Regardless of the type of node removal, network robustness in the YRD has improved over time. Shanghai remains the most robust city in terms of technological networks, while provincial capitals and regional centers such as Nanjing, Suzhou, Hangzhou, and Hefei have seen rapid improvements.
(3) Concerning the long-term robustness patterns in key cities, over the long term, Shanghai maintains the highest level of technological network robustness in the YRD, especially in response to targeted removals. While cities like Nanjing and Hangzhou perform well under random removal scenarios, their robustness against targeted removals remains relatively weak. Hefei, in particular, shows lower robustness in handling targeted attract.
(4) With regard to the impact of technological network structure on industrial resilience, regression analysis reveals a significant positive relationship between technological network robustness and industrial resilience. The greater the proportion of targeted node removal, the stronger the effect of network robustness on resilience. Among all measures, robustness under targeted removal shows the strongest positive impact. Moreover, related variety negatively affects industrial resilience, while unrelated variety has a significant positive effect. However, the influence of technological diversity on resilience is considerably weaker than that of network robustness.
6.2 Discussion
This study follows the classical analytical framework of regional economic resilience research by constructing an evaluation system for industrial resilience. Starting from the perspective of regional economic structure, it focuses on how technological factor endowments—as a key component of economic structure—influence regional industrial resilience. The study introduces two key innovations: First, building upon the traditional resilience framework, this research employs micro-level firm data to quantitatively assess regional industrial resilience across three process-oriented dimensions: resistance, recovery, and reconfiguration. This approach not only enriches the methods for measuring industrial resilience but also enhances the granularity and specificity of the analysis. Second, the study incorporates a novel network science perspective by introducing the concept and metrics of technological network robustness. This allows for a more refined depiction of regional technological network structures and provides a new lens through which to examine their effects on industrial resilience. By doing so, the study aims to offer fresh insights and understanding for resilience research in the context of regional industrial systems.
Based on the main findings, this study offers the following policy recommendations for optimizing technological network structures and enhancing industrial resilience in the YRD. First, strengthen protection of core technologies. The findings highlight that targeted removal of high-degree nodes significantly undermines network robustness. Therefore, safeguarding key technologies and ensuring that critical technical capabilities remain under local control is crucial for maintaining the structural integrity of technology networks and enhancing industrial resilience. Second, improve network robustness in key cities. Major cities in the YRD—especially regional hubs—must reinforce the robustness of their technological networks, particularly against targeted attacks on key nodes. Aside from Shanghai, most cities demonstrate inadequate robustness under such conditions. Even provincial capitals such as Nanjing, Hangzhou, and Hefei exhibit limited robustness, underscoring the urgent need to fortify the network structures of central cities. Third, leverage network structure for resilience enhancement. Technological network structure offers a promising pathway to improving regional industrial resilience. Enhancing network robustness (whether under targeted or random removal scenarios) and promoting unrelated variety in technology development are effective strategies to strengthen a region's capacity to withstand and adapt to external shocks.
7. Limitations and Future Research
Despite offering new empirical insights, this study has several limitations that provide directions for future research. First, the technological network constructed in this paper is based solely on patent co-occurrence and therefore captures knowledge relatedness between technological domains. It does not incorporate collaborative technological relationships, such as co-inventor networks, co-assignee networks, or inter-city joint patent applications. Future studies could build multi-layer or multiplex network structures that integrate both relatedness and collaboration networks to more comprehensively reflect regional technological structures. Second, although industrial resilience was measured through the processes of resistance, recovery, and reconfiguration, the analytical granularity can be further refined. Future research may explicitly distinguish adaptation from transformation/reconstruction, and track firm-level dynamics—such as entry, scaling, technological pivoting, exit, and re-entry—to capture micro-level path evolution and structural adjustment. Third, the robustness analysis primarily adopts degree-based random and targeted node attacks. Future work could incorporate alternative failure mechanisms, such as betweenness-based removal, eigenvector-based removal, or bridge-edge attacks, and further integrate core–periphery structure and modularity into robustness evaluation. In addition, simulating dynamic robustness under continuous or cascading shocks would better reflect real-world network failure processes. Finally, the Yangtze River Delta is a technologically advanced and economically leading region. Therefore, the external validity of the results should be tested in other Chinese urban agglomerations and international regions with different industrial and innovation structures. Comparative research will help determine whether the mechanisms identified in this paper hold across different development contexts. Overall, incorporating collaborative innovation networks, enriching robustness evaluation methods, refining resilience processes, and expanding comparative regional studies will help deepen the understanding of how technological network structures shape industrial resilience.
Funding Declaration: the National Natural Science Foundation of China, Grant/Award Number: 42201177, 42571209. Major Research Project in Philosophy and Social Sciences of Jiangsu Provincial Universities and Colleges (2024SJZD025)
A
Author Contribution
Juntao Tan and Yijia Chen conceived and wrote the main manuscript. Zixuan Wang was responsible for data collection and processing, and Fangdao Qiu supervised the revision and improvement of the paper.
A
Data Availability
This statement will replace any statement written within the manuscript and is the one that we will publish.
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