Spatial association network of economic resilience and its influencing factors: evidence from 31 Chinese provinces

The paper addresses how interprovincial economic resilience in China behaves as a spatially correlated networked system amid major external shocks (e.g., COVID-19, inflation, geopolitical conflicts) and China’s structural transformation. It underscores regional heterogeneity in geography, resources, and development that leads to uneven resilience to shocks, and argues that resilience connections now extend beyond simple geographic proximity into network forms. The study aims to accurately characterize the spatial association network of economic resilience across 31 provinces (2012–2020), clarify provincial roles in that network, and identify the drivers of these spatial linkages to enhance regional capacity to cope with shocks and promote sustainable national development.

Resilience originated in ecology (Holling, 1973) and was introduced to economics by Reggiani et al. (2002). Martin (2012) framed regional economic resilience across resistance/absorption, recovery, reorganization, and path creation. Broadly, definitions emphasize both the capacity to resist/adapt to shocks and to transform and create new development paths (e.g., Boschma, 2014; Tan et al., 2020). Measurement approaches include sensitive index methods using single indicators (e.g., GDP, unemployment, employment growth) but face drawbacks like limited applicability to small shocks and narrow variable sets. Composite index methods capture multiple dimensions (resistance, adaptation, transformation) with indicators such as GDP growth, GDP per capita, industrial diversification, openness, unemployment, investment, finance, industrial upgrading, education, and innovation (e.g., Cowell, 2013; Bristow and Healy, 2014; Hu et al., 2022). Factors shaping resilience include industrial structure, FDI, human capital, innovation, demographics, urbanization, and COVID-19 impacts. Spatially, studies using ESDA and spatial econometrics find significant spatial dependence and agglomeration, but prior work is often static, focuses on geographic contiguity only, and does not fully reveal structural patterns and non-neighbor spillovers in resilience networks. This study responds by adopting a complex systems and social network perspective to capture multi-scalar, non-contiguous spatial linkages.

Study area and period: 31 Chinese provincial-level regions, 2012–2020. Data sources include China Statistical Yearbook, China Industrial Statistical Yearbook, China Science and Technology Statistical Yearbook, China High Technology Industry Statistical Yearbook, and EPS Database. Economic resilience index: A composite system constructed across three dimensions—Resistance, Adaptation, and Transformation—with 13 indicators: GDP growth rate, GDP per capita, industrial structure diversification (DIV), foreign investment dependence, unemployment rate, total factor productivity; investment in fixed assets, ratio of deposit and loan balances of financial institutions, fiscal expenditure as a share of GDP; industrial upgrading level (HIS), science and technology expenditure, number of patents granted, and education expenditure. Indicator weights are determined via the entropy-TOPSIS method to avoid subjective weighting and information loss. DIV is computed using an entropy-like measure based on employment shares across industries; HIS weights primary/secondary/tertiary sector shares (scaled 1–3). TFP is calculated via DEA-Malmquist with real GDP (2012 constant prices) as output and labor (employment) and capital (proxied by real fixed-asset investment) as inputs. Foreign investment dependence is actual utilized FDI/GDP. Openness is total imports+exports/GDP. Human capital is average years of schooling. Physical capital stock is estimated via the perpetual inventory method. Technological innovation capacity is proxied by full-time equivalent of R&D personnel. Spatial association network construction: An improved gravity model is used to compute bilateral association strengths between provinces using GDP and the economic resilience index, adjusted by interprovincial geographic distance and province-specific contribution factors. The resulting gravity matrix is row-thresholded by each row’s mean to form a binary directed matrix (1 for ties stronger than the row mean, 0 otherwise), capturing directed association relations among provinces for each year. Network measures: Overall network metrics include network relevance (total number of ties), density (actual ties/maximum possible ties), hierarchy (asymmetry of accessibility), and efficiency (redundancy of links; lower indicates more stable network). Node-level metrics include degree centrality (in-degree and out-degree), betweenness centrality (control over paths/resource flows), and closeness centrality (distance to other nodes). A composite centrality index for each province is built by aggregating degree, betweenness, and closeness via entropy-TOPSIS. Spatial subordination association: A subordination (dependency) index is defined to extract the main direction and skeleton of linkages by quantifying the share of mutual gravitational force attributable to counterpart provinces. With a row threshold of 0.2, binary subordination ties are formed to build a directed subordination network, enabling identification of core-periphery dependencies and subgroup structures. Block model analysis: The spatial association network is partitioned into blocks (plates) to identify roles: benefit plate, overflow plate, bilateral spillover plate, and broker plate. Internal and spillover ties among plates are compared using density and similarity matrices to infer inter-plate relations. QAP regression: Because variables are relational and potentially collinear, a quadratic assignment procedure is used to assess how differences in geography (adjacency), openness, digital economy (constructed from IT workforce ratio, internet users ratio, and financial inclusion index), human capital, physical capital stock, and technological innovation affect the presence/strength of interprovincial resilience ties. Both unstandardized and standardized coefficients are reported with permutation-based significance. Spatial Markov chains: To study temporal dynamics of provincial roles, the composite centrality index is discretized into four classes (marginal, general, sub-core, core) using 70%, 100%, and 130% of the mean as thresholds. Markov and spatial Markov transition matrices (conditioning on neighbors’ status via spatial lags) quantify persistence and upward/downward mobility of provincial centrality categories over time.

- Economic resilience levels (2020) ranged from 0.217 to 0.647 across provinces (mean 0.346; SD 0.283), showing large interprovincial disparities and a stepwise pattern from east to central to northwest to northeast. Conversion (transformation) power exceeds the average in only 10, all coastal or central developed provinces. - Network evolution (2012–2020): Maximum possible ties = 930; actual ties peak at about 250, reflecting strong linkage. Network relevance and density were stable (2012–2014), declined (2014–2016), then rose steadily post-2016. Network hierarchy increased steadily after 2013. Network efficiency fluctuated between 0.6276 and 0.6460, implying about 37% redundant connections and, over time, increasing stability amid growing hierarchical ordering—consistent with policy shifts around the 12th and 13th Five-Year Plans and supply-side reforms. - Central nodes (2020): By composite centrality and its components, Jiangsu, Shandong, Guangdong, Hubei, and Shaanxi are the most influential aggregation and radiation centers. Jiangsu ranks first in degree, betweenness, and closeness. Betweenness is highly concentrated: nine provinces (Jiangsu, Guangdong, Shandong, Hubei, Beijing, Shaanxi, Sichuan, Hebei, Henan) account for ~76.7% of total betweenness, indicating strong control over interprovincial factor flows. - Spillover directions: Net reception/emission patterns suggest overall spillovers from west to east and north to south, with increasing polarization in the east-central coastal region. Some provinces (e.g., Fujian) show higher out-degree than in-degree partly due to missing cross-strait data. - Spatial transfer of centrality (2012–2020): Markov transitions show high stability for marginal (81.7%) and core (78.6%) categories. General and sub-core provinces exhibit greater mobility; sub-core provinces retain status only 36.1% of the time and shift upward to core with 30.6% probability. Spatial Markov results indicate adjacency to marginal or core neighbors stabilizes one’s category; adjacency to general or sub-core neighbors increases upward mobility opportunities but also downward risk. - Subordination network (2020): The main dependency skeleton forms geographically coherent subgroups rather than a single core. Subgroup I (Bohai Rim core with Inner Mongolia, Shanxi, Northeast extensions) is large but with less stable peripheries—an open model. Subgroup II (Yangtze River Delta: Jiangsu–Zhejiang–Shanghai–Anhui) is highly stable and introverted with strong mutual ties (pairwise affiliations often >0.3) and minimal external subordination ties. Most affiliations lie east of the Hu Line; western provinces struggle to form strong aggregation-based resilience due to sparse populations and weaker bases. - Block model (2020): Four plates: Plate 1 (Beijing–Tianjin–Hebei–Shanxi–Inner Mongolia–Liaoning–Jilin–Heilongjiang–Shandong–Henan) is a bilateral spillover plate with dense internal ties and notable external interactions; Plate 2 (Tibet–Shaanxi–Gansu–Xinjiang–Qinghai–Ningxia) is an overflow plate with more outward than inward ties; Plate 3 (Shanghai–Jiangsu–Zhejiang–Anhui–Fujian–Jiangxi–Hunan–Hubei) is a benefit plate receiving spillovers from others; Plate 4 (Guangdong–Guangxi–Hainan–Chongqing–Sichuan–Guizhou–Yunnan) is a broker plate balancing internal cohesion with active inter-plate connections. The overall network density in 2020 is 0.269, and internal connections within all plates exceed expected values. - QAP regression (explained variance ≈ 32.6%): Geographical proximity (std. coeff ≈ 0.532, p<0.001) and human capital differences (≈ 0.080, p≈0.013) promote resilience ties. Differences in openness (≈ -0.144, p≈0.001) and physical capital stock (≈ -0.111, p≈0.002) hinder network formation. Digital economy (≈ -0.035, p≈0.202) and technological innovation (≈ 0.035, p≈0.213) are not statistically significant in explaining tie formation in this framework and period.

The study shows that interprovincial economic resilience in China operates through a structured, hierarchical, and increasingly stable spatial network, aligning with theoretical views that resilience emerges from inter-node interactions rather than isolated region-specific attributes. The identification of key provincial hubs (e.g., Jiangsu, Shandong, Guangdong, Hubei, Shaanxi) explains how factor flows and policy diffusion can support broader regional recovery and adaptation after shocks. The contrasting subgroup dynamics—open, expansive linkages around the Bohai Rim versus stable, introverted cohesion in the Yangtze River Delta—indicate different pathways to building resilience: risk-sharing through broad affiliations versus deep internal integration. Spatial Markov evidence confirms that neighboring contexts shape the mobility of provinces within the network’s hierarchy, implying that targeted regional collaborations can alter provinces’ centrality status. The QAP results clarify that spatial proximity and human capital complementarities are crucial to forming resilience linkages, while disparities in external openness and physical capital can fragment the network—highlighting the importance of coordinated policies that manage openness-related risks and shift focus from mere capital accumulation toward efficient allocation and structural upgrading.

The paper develops a comprehensive economic resilience index for 31 Chinese provinces (2012–2020) and maps the spatial association network using an improved gravity model, social network analysis, block modeling, and Markov/spatial Markov methods. Main conclusions: (1) Since 2016, a tightly ordered hierarchical structure of resilience has consolidated, with spillovers trending from west to east and north to south; Jiangsu, Shandong, Guangdong, Hubei, and Shaanxi function as core aggregation and radiation centers. (2) The subordination linkage structure coalesces into geographic subgroups—especially the open Bohai Rim and introverted Yangtze River Delta—reflecting economic circle/urban cluster logics. (3) Proximity and human capital differences facilitate resilience ties, while disparities in openness and physical capital hinder them; digital economy and technological innovation variability show limited explanatory power in this setting. Policy recommendations include narrowing interprovincial resilience gaps through synergistic development, leveraging core provinces’ radiation effects, and enhancing the receptivity of marginal regions; implementing regionally differentiated policies focusing on overflow plates and strengthening two-way spillovers; and advancing economic circle strategies (e.g., expanding Yangtze River Delta advantages westward, stabilizing northern linkages, and promoting Chengdu–Chongqing integration) to balance national resilience. Future research could refine network construction (alternative thresholds/weighting), incorporate interregional trade and mobility data, explore sectoral sub-networks, and assess post-2020 dynamics to capture pandemic recovery and new policy phases.

- Visualization is provided for 2020 due to space constraints, while the analysis spans 2012–2020, which may limit direct visual inspection of earlier years’ structures. - The study is confined to 31 mainland provinces; cross-strait linkages (e.g., with Taiwan) are not included, which may affect provinces like Fujian where external relations are material but unobserved. - The binary network relies on row-mean thresholds and a fixed subordination cutoff (0.2), choices that may influence tie selection and subgroup detection. - Some hypothesized drivers (digital economy and technological innovation) were statistically insignificant in QAP for this period, suggesting either measurement limitations or temporal/contextual effects not captured by the current indicators. - Results are specific to 2012–2020 and to the chosen indicators and methods; generalizability beyond this time frame or to different spatial scales requires caution.