The global economic landscape is currently marked by significant systemic crises, including the COVID-19 pandemic, high inflation, and the Russo-Ukrainian conflict. For China, undergoing economic transformation, enhancing economic resilience is crucial for navigating these risks and promoting high-quality growth. However, regional disparities in China necessitate a nuanced understanding of economic resilience, recognizing its spatial correlations and network structures. Existing research on economic resilience often focuses on static perspectives or geographical proximity, neglecting the complex network interactions and the role of various factors beyond simple neighborhood effects. This study addresses these limitations by employing social network analysis (SNA) to model the spatial association network of economic resilience in China, considering its evolution and influencing factors. The study aims to provide a deeper understanding of resilience as an emergent property arising from the interactions of individual provinces, enhancing the ability to effectively respond to economic shocks and foster sustainable development.

The concept of "resilience," originating in systems ecology, has been increasingly applied to economics. While various definitions exist, the core concept encompasses a region's ability to withstand and adapt to shocks, as well as its capacity for self-adjustment and transformative change. Existing methods for measuring economic resilience include the sensitive index method (using variables like unemployment and GDP) and the composite index method (incorporating multiple dimensions of resilience). While the sensitive index method is limited by its reliance on large shocks and narrow variable selection, the composite index method offers a more comprehensive assessment. Influencing factors of regional economic resilience have been explored extensively, encompassing industrial structure, foreign investment, human capital, technological innovation, demographic structure, urbanization, and even the impact of events like the COVID-19 pandemic. The "growth pole theory" suggests that economic development originates from growth cores and spreads through networks, leading to symbiotic systems with high resilience. However, previous spatial correlation studies often lack a network perspective, focusing only on geographical proximity and neglecting the complex relationships between non-neighboring regions and the dynamic evolution of these relationships. This study employs SNA to overcome these limitations, providing a more comprehensive and dynamic analysis of the resilience network.

This study employs a multi-faceted methodology to analyze the spatial association network of economic resilience across 31 Chinese provinces from 2012 to 2020. First, a comprehensive index evaluation system for economic resilience is constructed, encompassing 13 indicators categorized into resistance, adaptation, and transformation. The entropy-TOPSIS method is used to determine the weights of these indicators, objectively assigning weights without data loss. Second, an improved gravity model is utilized to construct the spatial association network. This model considers both the economic resilience index and regional GDP of each province, along with geographical distance, to calculate the gravitational force between provinces. A binary matrix is then created based on a threshold value, representing the existence (1) or absence (0) of an association. Third, SNA is applied to characterize the network. Overall network characteristics (relevance, density, hierarchy, efficiency) are analyzed to understand the overall structure. Individual centrality measures (degree, betweenness, closeness) are used to assess the role of each province within the network. A novel concept of 'subordination' is introduced to represent the main direction of interprovincial linkages, resulting in a subordination association network that clarifies dependency relationships. Block model analysis is then used to classify provinces into four types based on their roles in the network (benefit plate, overflow plate, bilateral spillover plate, and broker plate). Fourth, to analyze the factors influencing the spatial association network, Quadratic Assignment Procedure (QAP) regression is employed to account for potential multicollinearity among relational data. The QAP analysis considers factors such as geographical proximity, openness, digital economy index, human capital, physical capital stock, and technological innovation capacity. Finally, spatial Markov chains are used to model the dynamic evolution of provincial centrality indexes and explore the influence of neighboring provinces' resilience levels on a province's resilience status.

The study reveals several key findings regarding the spatial association network of economic resilience in China. First, a hierarchical structure of resilience emerged after 2016, with Jiangsu, Shandong, Guangdong, Hubei, and Shaanxi standing out as central nodes. The centrality index, aggregated from degree, betweenness, and closeness centrality, shows a significant east-west and north-south gradient, reflecting regional disparities in resilience. Provinces are classified into four categories (marginal, general, sub-core, core) based on their centrality index. Second, the analysis of the spatial transfer characteristics of node centrality using Markov chains highlights the stability of marginal and core provinces compared to general and sub-core provinces. The study finds that being adjacent to marginal or core provinces maintains a province's centrality index category, while adjacency to sub-core or general provinces presents opportunities for upward mobility. The spatial spillover of resilience generally follows a west-to-east and north-to-south pattern. Third, the subordination analysis reveals that the spatial subordination network exhibits a hierarchical structure formed by subgroups of provinces with geographical proximity. The essence of interprovincial resilience linkage is the aggregation of economic circles and city clusters. The Bohai Rim region forms a large, but less stable, subgroup, while the Yangtze River Delta region demonstrates a stable, inward-focused structure. Fourth, the QAP regression analysis indicates that geographical proximity and human capital positively influence the formation of spatial associations, while differences in external openness and physical capital stock inhibit them. The digital economy and technological innovation capacity do not significantly influence spatial correlation.

The findings address the research question by providing a detailed characterization of the spatial association network of economic resilience in China, revealing its dynamic evolution and key influencing factors. The hierarchical structure of resilience highlights the uneven development across provinces and the role of specific regions as drivers of economic resilience. The spatial transfer analysis demonstrates the dynamic interplay between neighboring provinces' resilience and a province's own trajectory. The identification of geographical proximity and human capital as drivers of spatial association networks, coupled with the inhibiting effects of openness and physical capital differences, offers valuable insights into policy implications. The study's findings contribute to the broader understanding of economic resilience as a spatially correlated and evolving phenomenon, moving beyond simple geographical proximity to capture the complexity of network interactions. This nuanced understanding of regional resilience is crucial for informing effective economic policy in China.

This study provides a novel perspective on the spatial association network of economic resilience in China, using SNA to reveal a complex, dynamic, and geographically patterned network. Key findings highlight the emergence of a hierarchical structure, the importance of specific regions as central nodes, and the influence of various factors on spatial associations. Future research could explore the impact of specific policies on the network's structure and resilience, further refine the measurement of economic resilience, and extend the analysis to other national and regional contexts. The framework presented here can be applied to assess the resilience of other complex systems.

While the study offers a comprehensive analysis, some limitations exist. The data used are primarily macroeconomic, potentially overlooking micro-level factors that could influence resilience. The gravity model employed, while effective, might not perfectly capture all aspects of interprovincial economic interactions. Furthermore, the study focuses on China, limiting the generalizability of findings to other contexts with different institutional setups and economic structures.