Evolution and driving factors of the spatial association network of urban flood resilience in the Yangtze river delta urban agglomeration

1 Introduction

As complex territorial systems characterized by dense concentrations of population, industry, infrastructure, and ecological assets, cities are critical arenas in which disaster risks emerge, propagate, and are governed. In recent years, accelerating global climate change has increased both the frequency and uncertainty of extreme precipitation events [1]. Combined with the rapid expansion of urban construction land, increasing surface imperviousness, and the loss of natural water-retention spaces [2], these changes have made urban flooding increasingly characterized by sudden onset, compound effects, and spatial propagation. Compared with other natural hazards, urban flooding not only directly threatens lives and property but can also amplify socioeconomic impacts through transport disruptions, infrastructure failures, interruptions to industrial and supply chains, and the suspension of public services. To reduce the systemic losses caused by flooding, China has successively promoted sponge city development, upgraded urban drainage and flood-control infrastructure, and implemented initiatives to strengthen natural disaster prevention and mitigation capacity. It has also increasingly incorporated the concept of resilience into territorial spatial planning, integrated river-basin management, and emergency management [3]. Accordingly, the focus of urban flood governance research has gradually shifted from a narrow reliance on engineering defenses toward an integrated, whole-process approach that combines risk prevention, impact resistance, emergency response, post-disaster recovery, and adaptive improvement [4]. Against this backdrop, enhancing urban flood resilience has become an important priority for advancing resilient city development, safeguarding regional security, and achieving sustainable development. As a comprehensive concept encompassing the capacity of urban systems to withstand, resist, and recover from flood hazards, flood resilience is fundamental to a city’s ability to cope with flood-related shocks. A systematic examination of the spatial disparities, relational structures, and driving mechanisms of urban flood resilience can not only broaden the theoretical scope of disaster resilience research but also provide a theoretical foundation and practical support for coordinated regional disaster prevention and resilient city development.

A substantial body of research has examined urban flood resilience. First, in terms of research themes, existing studies have primarily focused on conceptualizing flood resilience, developing evaluation indicator systems, and identifying its influencing factors. Conceptually, urban flood resilience can be understood as the comprehensive capacity of an urban system to maintain its basic structure and core functions by resisting, absorbing, recovering from, and adapting to flood-related disturbances, while also undergoing post-disaster adjustment and improvement [5]. Regarding evaluation indicators, no universally accepted framework for assessing flood resilience has yet been established. Many studies assess urban flood risk using either the exposure–sensitivity–adaptive capacity (EAS) framework or the pressure–state–response (PSR) framework [6]. Other scholars have developed comprehensive evaluation systems based on the disaster cycle, incorporating dimensions such as resistance, absorption, recovery, and adaptation [7]. With respect to influencing factors, previous studies have demonstrated that urban flood resilience is shaped by economic development [8], infrastructure provision [9], baseline ecological conditions [10], and governmental capacity [11]. Some studies have employed spatial econometric models to confirm spatial spillover effects in flood resilience. In particular, the governance capacity of neighboring cities can significantly influence local resilience, indicating that resilience enhancement across regions is interconnected [12]. Second, in terms of spatial scale, research has gradually expanded from communities and individual cities to urban agglomerations, river basins, and provinces, with particular attention to spatial disparities and clustering patterns in flood resilience across regions [13, 14]. Methodologically, the entropy-weight method (EWM), analytic hierarchy process (AHP), technique for order preference by similarity to an ideal solution (TOPSIS), and principal component analysis have been widely used to measure resilience. Spatial autocorrelation analysis, spatial econometric models, and geographical detectors have primarily been employed to identify the spatial heterogeneity and determinants of flood resilience [15, 16]. Moreover, with the development of complex network methods, these methods have been widely and successfully applied to the analysis of economic linkages, population mobility, and ecological–environmental interactions [17]. A limited number of studies have also begun to examine the networked characteristics of urban disaster resilience from the perspectives of infrastructure interconnections, emergency cooperation, and risk propagation [5, 18], thereby offering a new analytical perspective for understanding regional flood governance.

Existing studies have established a solid foundation for the theoretical interpretation, comprehensive evaluation, and spatial governance of urban flood resilience; nevertheless, several gaps remain. First, most studies measure flood resilience on the basis of cities’ socioeconomic, ecological, and infrastructural attributes, focusing primarily on resilience levels and their geographical distribution while paying insufficient attention to whether stable spatial linkages form among cities. Second, much of the existing research relies on cross-sectional data or observations from a single point in time to analyze the spatial pattern of flood resilience. Consequently, relatively little attention has been devoted to the dynamic evolution of regional linkage networks, shifts in core nodes, and spillover patterns among network blocks. Third, studies of influencing factors have predominantly employed conventional regression analysis or spatial econometric models. Although these approaches can identify the effects of urban attributes on flood resilience, they are less capable of addressing the interdependence inherent in intercity relational data or explaining how socioeconomic disparities influence the formation of spatial networks. It is therefore necessary to move beyond the conventional treatment of cities as independent spatial units and adopt a relational network perspective to reveal the spatial linkage structure of urban flood resilience and its underlying drivers.

To address these gaps, this study examines 41 cities in the Yangtze River Delta (YRD). Drawing on resilience theory and life-cycle theory, it develops an evaluation indicator system for urban flood resilience across three dimensions: hazard sources, exposed receptors, and disaster-mitigation capacity. A modified Criteria Importance Through Intercriteria Correlation (CRITIC) method is used to estimate urban flood resilience, while social network analysis and quadratic assignment procedure (QAP) regression are employed to reveal the evolution and formation mechanisms of its spatial linkage network. The marginal contributions of this study are threefold. First, drawing on the “risk source–hazard-affected body–disaster-mitigation capacity” framework, it incorporates risk tolerance, emergency response, recovery and reconstruction, and adaptive enhancement into a unified evaluation framework, thereby providing a relatively comprehensive assessment of the performance of urban economic, social, ecological, engineering, and governance systems. Second, it extends the research focus from the level of urban flood resilience to the relational structure among cities. By identifying the directions of linkages among core nodes, peripheral nodes, and network blocks, this study addresses the limitations of relying solely on attribute data or geographic adjacency, which makes it difficult to explain long-distance intercity linkages. Third, it compares the effects of geographic proximity, urbanization, infrastructure, public attention to flooding, government finances, and institutional proximity on network linkages. In doing so, it reveals how multiple types of factors jointly shape the spatial network of flood resilience and provides a decision-making basis for optimizing emergency resource allocation, strengthening the radiating and driving capacity of key nodes, and improving the cross-regional collaborative flood-governance system in the YRD.

2 Methodology and data

2.1 Theoretical framework and indicator development

Urban flood resilience is not determined solely by precipitation intensity or drainage infrastructure; rather, it emerges from the interplay among natural hazard conditions, the urban built environment, demographic and economic activities, and disaster prevention and mitigation capacity. Extreme precipitation, water levels in river networks, and topographic conditions constitute the external drivers of flood disturbances [19]. High-density development, the expansion of impervious surfaces, and the concentration of population and assets alter cities’ exposure and sensitivity to flooding [20], whereas infrastructure provision, emergency management, and post-disaster recovery capacity shape the actual consequences and duration of flood impacts [21]. Therefore, urban flood resilience should not be assessed solely on the basis of flood probability, inundation severity, or direct losses. Instead, assessment should integrate hazard disturbances, the capacity of urban systems to withstand their impacts, and the regulatory role of disaster-mitigation capacity, while examining cities’ abilities to resist, absorb, respond to, recover from, and adapt to flooding throughout the disaster cycle. Accordingly, this study adopts the “risk source–hazard-affected body–disaster-mitigation capacity” framework [22] to analyze and evaluate urban flood resilience in terms of three dimensions: hazard pressure, exposure conditions, and disaster-mitigation capacity. Urban flood resilience is not independently determined by any single factor. Rather, it represents the overall state that emerges when flood disturbances affect a specific exposed system and are moderated by its disaster prevention and mitigation capacity. Applying this framework to urban flood resilience research effectively integrates hazard conditions, system vulnerability, and capacity building, thereby providing a relatively comprehensive theoretical foundation for developing the evaluation indicator system.

Under the “risk source–hazard-affected body–disaster-mitigation capacity” framework, urban flood resilience can be further disaggregated into three interrelated dimensions (Figure 1). First, risk sources represent the external pressures and direct triggers of urban flooding, primarily reflecting the intensity and likelihood of extreme precipitation, topographic variation, river and lake systems, and other flood-inducing conditions. Second, the hazard-affected body comprises the elements affected by flood disturbances, including urban economic activities, buildings and infrastructure, transportation systems, and the ecological environment. Its spatial exposure and structural vulnerability determine the extent to which the urban system is affected. Third, disaster-mitigation capacity refers to the comprehensive capacity of a city to reduce flood impacts. It encompasses pre-disaster resistance, emergency response during a disaster, and post-disaster recovery, thereby buffering external disturbances and facilitating the restoration of essential urban functions. Drawing on the “risk source–hazard-affected body–disaster-mitigation capacity” framework and disaster life-cycle theory, as well as relevant studies [23, 24], this study develops a comprehensive evaluation system for urban flood resilience (Table 1) and uses a modified CRITIC method to calculate the composite urban flood resilience index.

TABLE 1. Indicator system for assessing urban flood resilience.

Regarding indicator orientation, this study distinguishes between positive and negative indicators according to the underlying logic of the “risk source–hazard-affected body–disaster-mitigation capacity” framework. Indicators in the risk source dimension represent the external pressures associated with flood disturbances. Higher values of precipitation intensity, river-network density, and population density indicate greater hazard pressure or exposure and thus exert negative effects on urban flood resilience; these indicators are therefore specified as negative indicators. Within the hazard-affected body dimension, indicators such as per capita GDP, the number of industrial enterprises above the designated size, per capita disposable income of urban residents, and built-up area may, to some extent, imply greater asset exposure and a higher proportion of impervious surfaces. However, they primarily reflect a city’s economic foundation, resource-allocation capacity, and overall carrying capacity. Stronger economic capacity can provide material support for investment in disaster-prevention infrastructure, emergency material supplies, and post-disaster recovery and reconstruction. Accordingly, these indicators are specified as positive indicators. Infrastructure and ecological indicators, including drainage-pipe density, per capita road area, and green coverage, directly characterize a city’s capacity to withstand flood impacts and regulate stormwater and are likewise specified as positive indicators. Indicators in the disaster-mitigation capacity dimension directly reflect a city’s capacity to withstand disasters before they occur, respond during disasters, and recover and adapt afterward; they are therefore uniformly specified as positive indicators.

2.2 Study area and data sources

The YRD, located along China’s eastern coast and in the lower reaches and estuary of the Yangtze River, comprises Shanghai Municipality and the provinces of Jiangsu, Zhejiang, and Anhui, encompassing a total of 41 cities (Figure 2). The region features an interwoven landscape of plains, hills, dense river networks, and coastal landforms. Influenced by multiple weather systems, including the East Asian rainy season, typhoons, and severe convective weather, it is highly susceptible to flooding because of concentrated precipitation, abundant rivers and lakes, and generally low-lying terrain. Supported by a dense urban system, a well-developed transportation network, and a high concentration of population and economic activity, the YRD has become one of China’s most dynamic and highly urbanized regions, characterized by a high degree of openness and abundant innovation resources. It therefore occupies a strategically important position in China’s modernization and coordinated regional development. However, rapid urbanization and intensive land development in the YRD have led to the expansion of impervious surfaces, the loss of natural water-storage and retention spaces, and increasing pressure on urban drainage systems. Consequently, the risks associated with pluvial flooding, riverine flooding, and coastal storm surges increasingly overlap and interact. The cross-city propagation and cascading effects of flood hazards have also become more pronounced, constraining the safe and sustainable development of regional integration in the YRD. Enhancing urban flood resilience and optimizing its spatial association network are therefore essential to ensuring the safety and sustainable development of the YRD urban agglomeration.

The study uses 41 cities in the YRD urban agglomeration during 2011–2023 as its research sample. Precipitation data were obtained from the National Centers for Environmental Information (NCEI) of the U.S. National Oceanic and Atmospheric Administration (NOAA). The original data were stored by monitoring station and year. The data-processing procedure consisted of four steps. First, daily precipitation records from valid stations within China were extracted and consolidated for 2011–2023, and the measurement unit was converted from inches to millimeters. Second, spatial interpolation was conducted using the inverse distance weighting method to generate daily precipitation raster data at a spatial resolution of 1 km. Third, based on vector data for the administrative boundaries of prefecture-level cities in the YRD, the spatial average of the precipitation raster cells within each city was calculated to obtain daily precipitation series for each city. Finally, the data were aggregated annually to calculate three indicators: mean annual precipitation, maximum daily precipitation, and the number of heavy-rainfall days per year. Other data were obtained primarily from the China Statistical Yearbook, China City Statistical Yearbook, China Urban Construction Statistical Yearbook, and statistical yearbooks and development bulletins published by provincial and municipal governments. Some missing observations were imputed using linear interpolation and the autoregressive integrated moving average (ARIMA) model. Specifically, linear interpolation was applied to indicators with missing rates below 5%, whereas ARIMA-based time-series forecasting was used to impute indicators with relatively high missing rates or pronounced temporal trends. After imputation, the missing rate for all indicators was reduced to zero, thereby ensuring the completeness and temporal comparability of the panel data.

2.3 Research methods

2.3.1 Modified CRITIC method

The improved CRITIC method is suitable for the comprehensive evaluation of multidimensional systems. It determines indicator weights by jointly considering indicator variability and conflict. Unlike the conventional CRITIC method, which uses the standard deviation to measure variability, this study employs the coefficient of variation—that is, the ratio of the standard deviation to the mean—to quantify indicator variability. This approach eliminates the interference caused by differences in measurement units and mean levels when comparing the degree of fluctuation across indicators. Indicator conflict is measured based on the Pearson correlation coefficients between indicators. To ensure the temporal comparability of the measurement results from 2011 to 2023, panel-pooled standardization and a fixed-weight strategy are adopted. The specific procedures and calculation formulas are provided in Ref. [36].

2.3.2 Kernel density estimation

Kernel density estimation is a nonparametric method used to characterize the distribution and dynamic evolution of a variable. It requires no prior assumptions regarding the form of the sample distribution and can intuitively reveal distributional characteristics such as location, peakedness, and dispersion. It also offers high fitting accuracy and robust results. This study employs kernel density estimation to examine the overall distribution and spatiotemporal evolution of urban flood resilience in the YRD and to identify its patterns of agglomeration and differentiation. The kernel density function is calculated as shown in Equation 1:where N is the number of observations; x _i denotes an independent and identically distributed observation; K is the Gaussian kernel function; h is the bandwidth.

f x = 1 N h ∑ i = 1 N K x i − x ¯ h (1)

2.3.3 Modified gravity model

The modified gravity model integrates urban scale, development level, and spatial distance into a unified analytical framework to estimate the potential strength of intercity spatial interactions. Because urban flood resilience linkages are shaped not only by geographical distance but also by population concentration, economic scale, and resilience levels, this study draws on previous research [37] and applies a modified gravity model to quantify the strength of flood resilience linkages among cities in the YRD. The model is specified as shown in Equation 2:where R _*i*j denotes the strength of the spatial linkage between cities i and j;H _*i* and H _*j* represent their respective levels of urban flood resilience; K _*i*j is the correction coefficient; and D _*ij* is the geographical distance between the two cities. P _*i* and P _*j* denote the permanent resident populations of cities i and j, respectively; G _*i* and G _*j* represent their gross domestic product (GDP); and gi and gj denote their GDP per capita. To exclude interference from weak intercity linkages, following Liu et al. [38], the mean linkage strength in each city’s spatial association matrix is used as the threshold. It should be noted that the intercity flood-resilience association matrix derived from the modified gravity model represents a potential spatial association structure among cities rather than the actual movement of materials and personnel or the observed occurrence of governance cooperation. The network reflects the structural conditions under which factor interactions and risk transmission may occur among cities at the theoretical level. Accordingly, all subsequent analyses are based on the potential associations estimated by the model.

R i j = K i j G i P i H i 3 G j P j H j 3 D i j g i − g j 2 , K i j = H i H i + H j (2)

2.3.4 Social network analysis

Social network analysis conceptualizes cities as “actors” within a network and uses inter-node relationships to represent their spatial linkages. It is particularly suitable for identifying the structural patterns and evolutionary dynamics of complex relational systems [39]. This study applies social network analysis to systematically examine the structural characteristics and temporal evolution of the spatial association network of urban flood resilience from two perspectives: the overall network structure and individual nodal characteristics. The specific indicators are presented in Table 2.

TABLE 2. Indicators for analyzing spatial association characteristics.

2.3.5 QAP analysis

To identify the factors driving the spatial association network of urban flood resilience in the YRD, this study employs the Quadratic Assignment Procedure (QAP) for regression analysis. QAP is a nonparametric method designed to examine relationships between matrices. By using permutation-based significance tests, it accounts for the interdependence of relational data and reduces estimation biases associated with multicollinearity and potential endogeneity. Accordingly, QAP regression is used to assess the significance of the explanatory-variable difference matrices and thereby reveal the mechanisms underlying the formation of the spatial association network. The model is specified as shown in Equation 3:

Q = f D i s , U r b a n , Inf , A t t , F i s , I n s (3)

Where Q denotes the binary spatial association matrix of urban flood resilience, derived from the modified gravity model described above and dichotomized using the mean association strength as the threshold; Dis is the geographical-proximity matrix; Uban is the difference matrix of urbanization levels; Inf is the difference matrix of infrastructure levels; Att is the difference matrix of public attention to flood disasters; Fis is the difference matrix of fiscal self-sufficiency rates; and Ins is the institutional proximity matrix.

3 Results and discussion

3.1 Spatiotemporal patterns of urban flood resilience

3.1.1 Temporal evolution characteristics

Figure 3 illustrates the overall evolution of urban flood resilience in the YRD from 2011 to 2023. Over the study period, resilience exhibited a fluctuating upward trend. From 2011 to 2014, the mean urban flood resilience score in the YRD increased from 0.190 to 0.223. The regional resilience level declined slightly in 2015, followed by a gradual recovery between 2016 and 2018, reaching 0.239 in 2018. This period coincided with the continued advancement of YRD regional integration, ongoing improvements in urban flood-control and drainage infrastructure, and growing attention among local governments to flood prevention and emergency management. These developments may have contributed to the enhancement of urban flood resilience across the region. Urban flood resilience in the YRD decreased marginally in 2019. From 2020 to 2023, however, the regional resilience level increased steadily, reaching 0.277 in 2023. During this period, the YRD integration strategy was implemented more extensively, while institutional arrangements among the three provinces and Shanghai Municipality were progressively strengthened in areas such as coordinated river-basin management, flood control and drainage, emergency response, and cross-regional governance. The timing of these developments coincided with the sustained improvement in urban flood resilience, potentially indicating that coordinated regional development played a positive role in resilience building. At the provincial and municipal levels, Shanghai consistently maintained a relatively high level of resilience, although it experienced pronounced interannual fluctuations. Zhejiang generally ranked second and followed a fluctuating upward trajectory, whereas Jiangsu showed comparatively steady improvement. Anhui had the lowest initial resilience level but achieved substantial growth, approaching Jiangsu’s level by the end of the study period. Overall, urban flood resilience improved across the three provinces and Shanghai Municipality, although the pace and magnitude of change varied. The temporal pattern was characterized by Shanghai’s sustained leadership, Zhejiang’s steady improvement, Jiangsu’s gradual growth, and Anhui’s rapid catch-up.

Figure 3A presents the kernel density distributions of urban flood resilience in the YRD. In terms of distributional position, the curves generally shifted to the right between 2011 and 2023, indicating a sustained improvement in urban flood resilience, consistent with the trend in the regional mean. Regarding distributional shape, the curve for each year exhibits a pronounced primary peak. Although the height of this peak fluctuated over time, the distributions gradually flattened, indicating changes in the concentration of urban flood resilience. This pattern suggests that intraregional disparities did not narrow in parallel with the overall improvement in resilience. The distributions are predominantly right-tailed, with a marked extension toward the high-value end. During the later years, the low-value end shifted rightward along with the center of the distribution, while the high-value end remained extended. This pattern indicates that low-resilience cities improved over time, although some high-resilience cities retained their leading advantages. Minor secondary peaks appeared in several years; however, they were neither sufficiently distinct nor persistent to form a stable bimodal distribution. Therefore, although urban flood resilience in the YRD exhibited some degree of stratification during the study period, there is no evidence of pronounced or persistently intensifying polarization. Taken together, the shifts in distributional position, shape, and tail characteristics reveal a pattern of gradient differentiation amid an overall improvement in resilience: high-resilience cities maintained their leading positions, cities with low and moderate resilience gradually caught up, and intercity disparities continued to undergo periodic adjustments.

3.1.2 Spatial evolution characteristics

To further examine spatial disparities in urban flood resilience across the YRD, the resilience scores were classified into five categories—low, relatively low, medium, relatively high, and high—using the natural breaks (Jenks) method (using uniform breakpoints derived from the full sample for classification). Figure 4 presents their spatial distributions in 2011, 2017, and 2023. Overall, the resilience categories of most cities increased during the study period. The spatial pattern shifted from the widespread distribution of low- and relatively low-resilience cities to the predominance of relatively high- and high-resilience cities. Urban flood resilience generally exhibited a southeast–northwest gradient, with higher levels in southeastern coastal areas and lower levels in the northwestern inland areas. Coastal areas and regional central cities displayed notable advantages, which gradually extended to surrounding cities.

In 2011, urban flood resilience was generally low across the YRD. Low- and relatively low-resilience cities were primarily clustered in northern and western Anhui and northern Jiangsu, forming spatially contiguous areas. Cities in the medium-to-high categories were concentrated along the Shanghai–Nanjing–Hangzhou–Ningbo corridor. Shanghai, Nanjing, Hangzhou, and Ningbo were classified as high or relatively high, while Hefei, Suzhou, Wuxi, and their neighboring cities also exhibited comparatively high resilience. At this stage, high-resilience cities were few and spatially dispersed, with no extensive contiguous high-value areas. Consequently, marked differences remained between regional central cities and peripheral cities. By 2017, the number of low-resilience cities had decreased substantially, while the spatial coverage of cities classified as medium or above continued to expand. Shanghai, Nanjing, Hangzhou, and Ningbo maintained relatively high levels of resilience, and high-value areas extended outward along the Shanghai–Nanjing and Shanghai–Hangzhou–Ningbo corridors. Spatial clustering also became increasingly pronounced in southern Jiangsu and northern Zhejiang. Meanwhile, the resilience categories of Hefei and cities along the Anhui section of the Yangtze River increased, forming a new relatively high-value area in the central and western YRD. Nevertheless, some cities in northern and western Anhui and northern Jiangsu remained in the lower categories, and the spatial gradient between the southeastern coastal areas and the northwestern inland areas persisted. By 2023, the spatial pattern of urban flood resilience had undergone further adjustment. Low- and relatively low-value areas had largely disappeared, whereas relatively high- and high-resilience cities were widely distributed. High-value areas expanded from a small number of regional central cities to southern Jiangsu, central and southern Anhui, and most of Zhejiang, gradually evolving from isolated clusters into extensive contiguous areas. Cities in northern Jiangsu and northern Anhui also moved from the low or relatively low categories to the medium or relatively high categories, substantially reducing the region’s low-resilience deficits. Although disparities between the northwestern and southeastern parts of the region remained, the continued contraction of low-value areas and the contiguous expansion of high-value areas indicate an increasingly balanced spatial distribution of urban flood resilience across the YRD.

3.2 Analysis of the strength of intercity linkages in urban flood resilience

To examine the spatial linkages of urban flood resilience across the YRD, this study employs a modified gravity model to estimate the strength of resilience linkages between cities. ArcGIS is then used to visualize the spatial linkage networks for 2011, 2017, and 2023.

As shown in Figure 5, the urban flood resilience network evolved from a sparse to a dense structure and from localized clustering to polycentric interaction over the study period. Regional associations have gradually transcended the constraints imposed by geographical proximity and administrative boundaries, while network linkages between core cities and secondary nodes have continued to strengthen. This finding indicates that central cities such as Shanghai, Nanjing, Suzhou, and Hangzhou possess the structural conditions necessary to disseminate flood-governance experience and share emergency resources with other cities. At the same time, secondary cities have increasingly gained opportunities to become embedded in the regional resilience-cooperation system. The network’s evolution from a dispersed structure toward polycentric coordination suggests that the structural foundation for coordinating and allocating flood-control resources across cities in the YRD has continued to strengthen. Both the driving influence of core nodes and the integration of peripheral nodes into the network have improved to varying degrees, thereby providing structural support for enhancing urban flood resilience across the region.

Spatially, the linkage network among core cities was substantially denser than that in peripheral areas, suggesting that geographical disparities in economic development, infrastructure conditions, and policy resource allocation continued to shape the spatial configuration of intercity flood resilience linkages. In 2011, the spatial network was generally sparse, with strong and core linkages concentrated among Shanghai, Suzhou, Wuxi, and Nanjing, forming distinct small-scale clusters. Some cities in Zhejiang had established linkages with the Shanghai–Jiangsu core area, although their linkage strength remained relatively limited. Most cities in northern Anhui, northern Jiangsu, and southwestern Zhejiang were located at the periphery of the network. By 2017, intercity linkages had strengthened considerably, and the influence of Nanjing, Suzhou, Shanghai, and Hangzhou had become more pronounced. Cross-provincial linkages among Shanghai, Jiangsu, and Zhejiang grew increasingly dense, while Hefei and cities along the Anhui section of the Yangtze River became more integrated into the network. Consequently, the spatial structure gradually shifted from isolated clusters to corridor-like connections. By 2023, with the deepening of regional collaborative governance, strong linkages had expanded further into central and northern Jiangsu, central Zhejiang, and cities along the Anhui section of the Yangtze River. A denser, multilevel network emerged between core and secondary cities. Although network polarization declined, weak linkages continued to predominate in some cities in western and northern Anhui and southwestern Zhejiang. Overall, the YRD has developed a spatial linkage pattern of urban flood resilience characterized by the leadership of core cities, the support of regional nodes, and the gradual integration of peripheral cities.

3.3 Structural characteristics of the spatial association network of urban flood resilience

3.3.1 Overall network structure

To characterize the overall structure and evolution of the spatial association network of urban flood resilience in the YRD, this study used UCINET to calculate network density, connectedness, hierarchy, and efficiency. The results are presented in Figure 6.

From 2011 to 2023, network density fluctuated between 0.3134 and 0.3439, exhibiting an overall upward trend. It increased from 0.3146 in 2011 to 0.3427 in 2017, temporarily declined during 2018–2019, and subsequently resumed its growth, reaching 0.3439 in 2022 and remaining stable in 2023. Although the regional network has not yet attained a high density, its level at the end of the period was higher than at the beginning. This suggests that, with the deepening of YRD integration, potential intercity linkages in resource allocation, emergency-management cooperation, and risk-information sharing have gradually transcended administrative boundaries, thereby strengthening spatial associations in urban resilience. Nevertheless, the network density still has considerable room for improvement.

Network connectivity remained at 1 throughout the study period, indicating that the urban flood-resilience network in the YRD has strong connectivity. All cities were able to participate in regional interactions through direct or indirect pathways, and no node was completely isolated from the network. This persistent region-wide connectivity provides a structural foundation for the cross-city allocation of flood-control resources and coordinated disaster-risk governance. It also suggests that changes in the resilience of individual cities may be transmitted to other areas through network linkages.

Notably, network hierarchy remained at 0 throughout the study period, indicating that no strict hierarchical structure had yet emerged. Although cities such as Shanghai, Nanjing, Suzhou, and Hangzhou possessed strong capacities for resource concentration and regional spillover within the network, intercity linkages did not exhibit a pattern of one-way dependence; instead, horizontal collaboration remained an important feature of network operation. Network efficiency fluctuated downward from 0.7205 in 2011 to 0.6897 in 2023. This change indicates that redundant linkages within the network increased, while the pathways for transmitting information, technology, and emergency resources became more diversified, thereby enhancing the substitutability of network connections.

Overall, the urban flood-resilience network in the YRD has developed a structure characterized by region-wide connectivity, weak hierarchical constraints, and a growing number of alternative pathways. Nevertheless, network density still has room for improvement, and the network foundation for deeper intercity collaboration requires further consolidation.

3.3.2 Individual network structure

To examine the position and role of each city in the spatial association network of urban flood resilience in the YRD, degree centrality, closeness centrality, and betweenness centrality in 2011 and 2023 were selected for comparative analysis. The results are presented in Table 3.

TABLE 3. Individual network characteristics of spatial associations in urban flood resilience in the Yangtze River Delta.

First, degree centrality increased from a regional average of 31.46–34.39, indicating a strengthening of direct intercity linkages. Wuxi, Suzhou, Shanghai, Changzhou, and Nanjing consistently ranked among the highest-value cities and maintained relatively extensive connections within the regional network. Wuxi’s degree centrality declined from 95 to 90 but remained the highest in the region. Suzhou’s value decreased to 85, while Shanghai and Changzhou both reached 80 in 2023; Nanjing increased from 67.5 to 75. These cities possess relatively strong economic foundations, infrastructure systems, emergency-management capacities, and resource-integration capabilities, enabling them to establish extensive connections with other nodes. Yangzhou’s degree centrality rose from 27.5 to 55, while Suzhou (Anhui), Bozhou, and Taizhou also recorded varying degrees of improvement, suggesting that network linkages have gradually extended toward secondary nodes. By contrast, Hangzhou, Hefei, and Ningbo experienced declines, indicating a weakening of their advantages in terms of direct connectivity.

Second, the distribution of closeness centrality was broadly consistent with that of degree centrality. In 2011, Wuxi, Suzhou, and Shanghai recorded values of 95.238, 93.023, and 86.957, respectively, and they remained among the leading cities in 2023. Changzhou and Nanjing increased to 83.333 and 78.431, respectively, indicating further improvements in network accessibility. These cities were connected to other nodes through relatively short paths and therefore occupied highly accessible positions within the network. This structure facilitated information exchange, the allocation of emergency resources, and the diffusion of governance experience. Yangzhou’s closeness centrality increased markedly from 57.971 to 68.966, whereas the relatively low values recorded by cities such as Tongling and Zhoushan indicate that their integration into the regional network remained limited.

Finally, in terms of betweenness centrality, Wuxi, Suzhou, and Shanghai consistently served as important bridges within the network, with values of 11.425, 10.161, and 11.226, respectively, in 2023. The values for Changzhou and Nanjing increased from 5.635 to 6.449 to 8.869 and 8.166, respectively, indicating a substantial enhancement in their capacity to mediate key network pathways. Hangzhou’s value declined from 6.777 to 3.437, reflecting a weakening of its intermediary position. Most peripheral cities exhibited relatively low betweenness centrality and had not yet developed stable cross-regional transmission functions. Overall, the urban flood-resilience network in the Yangtze River Delta remains dominated by core cities along the Shanghai–Nanjing corridor. At the same time, secondary nodes such as Yangzhou have accelerated their integration into the network, and the network structure has gradually evolved toward greater coordination among multiple nodes.

Overall, the urban flood resilience network in the YRD remained dominated by the core cities along the Shanghai–Nanjing corridor. However, secondary nodes such as Yangzhou became increasingly integrated, and the individual-level network structure gradually evolved toward coordination among multiple nodes.

3.4 Block model analysis

Using data from 2011 to 2023, the 41 cities in the YRD were classified into four blocks through the CONCOR method. Based on the expected and actual proportions of internal ties and the receipt and transmission of ties within each block, Blocks I and II were classified as net spillover blocks in 2011, Block III as a bidirectional spillover block, and Block IV as a net beneficiary block. In 2023, the roles of Blocks I and II remained unchanged, whereas Block III shifted to a net beneficiary block and Block IV became a bidirectional spillover block. No broker block emerged during the study period. The transmission relationships among the four blocks are illustrated in Figure 7. As shown in Table 4, the network contained 345 ties in 2011, including 55 within-block ties and 290 between-block ties, accounting for 15.94% and 84.06% of the total, respectively. By 2023, the total number of ties had increased to 388. The number of within-block ties decreased to 51, whereas that of between-block ties rose to 337, accounting for 13.14% and 86.86%, respectively. Compared with 2011, the network gained 43 ties by 2023, with most of the increase occurring between blocks. This finding indicates that cross-block associations in urban flood resilience across the YRD continued to strengthen, while within-block agglomeration weakened.

TABLE 4. Inter-block spillover effects in the spatial association network of urban flood resilience in the Yangtze River Delta.

Specifically, Block I comprised 21 cities in 2011. It transmitted 150 external ties but received only 36, making it the block with the largest spillover effect in the network. Of these ties, 120 and 27 were directed toward Blocks III and IV, respectively, indicating a relatively concentrated pattern of outward linkages. Block II also exhibited net spillover characteristics, with most of its external ties directed toward Block III. Block III, comprising Shanghai, Suzhou, Wuxi, Changzhou, Nanjing, and Zhenjiang, had an actual internal-tie proportion of 19.64%, exceeding the expected value of 12.5%. It also received 167 external ties, making it the principal bidirectional spillover block during this period. Block IV comprised only Ningbo, Hangzhou, and Tongling. Stable internal ties had not yet formed within this block, which primarily received linkages from other blocks and was therefore classified as a net beneficiary block.

By 2023, Blocks I and II continued to perform the principal output function, although the destinations of their ties had changed. Block I transmitted 82 ties to Block III, substantially fewer than in 2011, while its ties to Block IV increased to 75. Block II transmitted 49 ties to Block IV, indicating that network linkages were becoming increasingly concentrated in Block IV. During the same period, the actual proportion of internal ties in Block III declined to 7.69%. It received 99 ties, exceeding the 60 ties it transmitted externally, and consequently shifted from a bidirectional spillover block to a net beneficiary block. The number of cities in Block IV increased from three to six, with core cities such as Shanghai, Suzhou, and Wuxi joining the block. Its internal ties increased to eight, and its actual internal-tie proportion reached 16.33%. Meanwhile, Block IV received 130 ties from the other blocks and became a bidirectional spillover block. Overall, the composition of the net spillover blocks remained relatively stable, but the network’s principal receiving center shifted from Block III to Block IV. Moreover, inter-block associations gradually evolved from a relatively concentrated pattern toward multidirectional transmission.

3.5 Driving factors of the spatial association network of urban flood resilience

3.5.1 Selection of driving factors

Spatial associations in urban flood resilience are the combined outcome of the cross-regional flows of risk information, emergency resources, infrastructure functions, and governmental governance capacity. Drawing on relevant studies [40–42] and considering the formation characteristics of these spatial associations, this study selects the following driving factors: (1) Geographical proximity (Dis): Tobler’s First Law of Geography suggests that geographically proximate cities generally exhibit more frequent factor exchanges. Shorter distances reduce the costs of information transmission, material transportation, and emergency coordination, and may therefore produce stronger spatial association effects. (2) Difference in urbanization level (Urban): Urbanization reshapes population concentration, risk exposure, and governance demand. Cities at different stages of development may establish resilience linkages through functional complementarity and intercity factor flows. (3)Difference in infrastructure level (Inf): Infrastructure provides the physical foundation for cross-regional emergency response and coordinated public service provision. Differences in infrastructure conditions may create linkages between resource supply and emergency response demand. (4) Difference in public attention to flood disasters (Att): Public attention reflects societal risk perception and the social foundation for disaster-prevention mobilization. Regional differences in public attention may facilitate the cross-regional diffusion of disaster information and response experience. (5) Difference in fiscal self-sufficiency (Fis): The fiscal self-sufficiency rate reflects the capacity of local governments to independently raise and allocate resources. Differences in fiscal capacity may strengthen resource dependence among cities and promote the intercity flow of disaster-prevention funds and governance experience. (6) Institutional proximity (Ins): Shared administrative affiliation facilitates policy coordination, information sharing, and joint action, thereby reducing the coordination costs of cross-city flood governance. Given the relational nature of the research object, city-level attributes are transformed into difference matrices. Spatial-distance and institutional-proximity matrices are employed to capture geographical constraints and administrative linkages, respectively. The measurement methods for the driving factors are presented in Table 5.

TABLE 5. Driving factors of the spatial association network of urban flood resilience.

3.5.2 QAP regression analysis

To clearly identify the evolution of the effects of various factors on the spatial associations of urban flood resilience in the YRD, QAP regressions were conducted for three selected years: 2011, 2017, and 2023. These years were selected for the following reasons. As the initial year of the study period, 2011 reflects the early-stage drivers of network formation. As a mid-period observation, 2017 coincided with the accelerated implementation of the YRD integration strategy, thereby capturing changes in the policy environment. As the terminal year, 2023 reflects the characteristics of spatial associations as the network approached maturity. Together, these 3 years provide relatively even coverage of the study period and effectively reveal the temporal evolution of the underlying drivers. The significance of each influencing factor was tested using 2,000 random permutations. The results are presented in Table 6.

TABLE 6. Results of the QAP regression analysis.

The specific findings are as follows: (1) Geographical proximity consistently exerted a significant positive effect, with standardized coefficients of 0.135, 0.158, and 0.120, respectively. This finding indicates that geographically adjacent cities are more likely to establish intercity linkages. When cities are located closer to one another, their associations in terms of flood resilience tend to be stronger, as spatial proximity may facilitate the sharing of resilience-related resources, emergency coordination, and the diffusion of governance experience. (2) Differences in urbanization levels exerted significant positive effects in all 3 years, with standardized coefficients of 0.070, 0.048, and 0.211, respectively. The effects were significant at the 5% level in 2011 and 2017 and at the 1% level in 2023. This finding indicates that disparities in urbanization levels generally contribute to stronger intercity associations in urban flood resilience, reflecting a certain degree of functional complementarity among cities at different stages of development. One possible explanation is that highly urbanized cities tend to concentrate greater financial resources, advanced technologies, and specialized emergency-response capacity, whereas less urbanized cities generally retain more ecological space and have stronger demands for external disaster-prevention resources and governance experience. Differences in resource endowments and governance capacities may therefore provide the basis and driving force for the intercity flow of factors and collaborative action in flood-risk management and resilience-oriented urban development. (3) Differences in infrastructure levels exerted significant positive effects in 2011 and 2017, with standardized coefficients of 0.118 and 0.185, respectively. This result suggests that cities with different infrastructure conditions may establish linkages through emergency assistance and the sharing of public services. In 2023, however, the coefficient declined to 0.012 and was no longer statistically significant, possibly indicating that the influence of infrastructure disparities weakened as regional infrastructure connectivity and interoperability improved. (4) Differences in public attention consistently exerted significant positive effects, although the standardized coefficient declined from 0.442 to 0.242. This finding suggests that differences in public concern regarding disaster risks may, to some extent, promote the dissemination of disaster-related information and the exchange of disaster-prevention experience. However, as early-warning systems and information-sharing mechanisms have gradually improved, the influence of this factor has diminished. (5) Differences in fiscal self-sufficiency had significant positive effects in all 3 years, with standardized coefficients of 0.230, 0.341, and 0.226, respectively. Cities with different fiscal capacities may exhibit complementary relationships in terms of funding provision, emergency support, and governance needs. Such differences can potentially strengthen the interregional flow of resources for disaster prevention and mitigation. Nevertheless, this effect declined after reaching a peak in 2017. (6) Institutional proximity consistently exerted a significant positive effect, with standardized coefficients of 0.205, 0.130, and 0.136, respectively. This result indicates that cities within the same province may be more likely to establish flood-resilience linkages. Although this effect persisted throughout the study period, its coefficient generally declined, possibly reflecting the continuous deepening of cross-provincial flood-control cooperation and basin-wide joint prevention and control in the YRD. Consequently, the constraints imposed by provincial administrative boundaries on intercity resilience linkages may have weakened.

Overall, the formation mechanism of spatial associations in urban flood resilience across the YRD has undergone notable changes. During the initial stage of the study period, intercity linkages were influenced primarily by public attention to disaster risks, geographical conditions, and administrative affiliation. As regional integration deepened, fiscal resource allocation, the functional division of cities, and cross-regional network connectivity gradually became more important drivers. Cities do not establish linkages solely because of similarities in their attributes; differences in capabilities and governance needs can also promote resource exchange and coordinated action. Consequently, resilience associations have shown a tendency to evolve from a network dominated by individual factors toward a multi-factor, synergistic, and cross-regional complementary structure.

4 Conclusions and policy implications

4.1 Conclusions

From the perspective of urban flood resilience, this study measures the flood resilience of 41 cities in the YRD from 2011 to 2023. By integrating a modified gravity model, social network analysis, block mode, and QAP regression, it systematically examines the spatiotemporal evolution, association intensity, network structure, and driving factors of urban flood resilience. The main conclusions are as follows.

• Urban flood resilience in the YRD exhibited an overall fluctuating upward trend, forming a spatial pattern centered on Shanghai and extending along the Shanghai–Nanjing and Shanghai–Hangzhou development axes. Shanghai and Zhejiang generally maintained relatively high levels of resilience, Jiangsu improved steadily, and Anhui experienced rapid growth. Nevertheless, regional disparities persisted.
• Intercity resilience associations have become increasingly close, with the network structure evolving from localized agglomeration toward a cross-regional, networked configuration. Relying on their accumulated resources and governance capacity, core cities possess the structural conditions necessary to diffuse flood-governance capabilities outward. The degree of network embeddedness of some peripheral cities has also improved; however, the strength of intercity associations and the balance of network connectivity still require further enhancement.
• Network connectivity and stability gradually increased, accompanied by an emerging pattern of multi-node coordination. Shanghai, Suzhou, Wuxi, Changzhou, and Nanjing occupied central positions and served as important hubs and pathway connectors within the network. By contrast, cities such as Tongling and Zhoushan remained relatively peripheral, and their capacity to participate in the network requires further enhancement.
• The block-model results indicate that the spatial association network of flood resilience in the Yangtze River Delta can be divided into two net-outflow blocks, one bidirectional-outflow block, and one net-beneficiary block. During the study period, the composition of the net-outflow blocks remained relatively stable, while the center of gravity for receiving network associations shifted from Block III to Block IV. The proportion of cross-block network linkages continued to increase, although no broker block responsible for intermediary or bridging functions had yet emerged within the network.
• The analysis of influencing factors indicated that geographical proximity, differences in urbanization levels, infrastructure development, public attention, fiscal self-sufficiency, and institutional proximity exerted differentiated effects on the spatial associations of urban flood resilience. Geographical proximity consistently had a significant positive effect. Differences in urbanization levels, public attention, and fiscal self-sufficiency also significantly promoted intercity resilience associations. The effect of infrastructure disparities changed from significant to nonsignificant, whereas institutional proximity remained significant throughout the study period, despite an overall decline in its coefficient.

4.2 Policy implications

The above findings demonstrate that urban flood resilience in the YRD is characterized by pronounced cross-regional linkages. Regional flood-resilience governance should therefore move beyond the traditional model of territorially bounded management by individual cities and establish a systematic governance framework featuring differentiated strategies, multilevel coordination, and cross-regional collaboration.

First, given the uneven development of regional resilience, Shanghai’s leading role as a core hub should be further strengthened, and the Shanghai–Nanjing and Shanghai–Hangzhou development axes should be leveraged to establish high-level demonstration corridors for flood resilience. Cities in Zhejiang with established advantages should consolidate the achievements of their disaster-prevention systems, while Jiangsu should steadily promote infrastructure upgrading and quality improvement. Anhui should continue to receive preferential policy and resource support to sustain its rapid improvement. Through differentiated resource allocation, disparities in resilience development across provinces and cities can be gradually narrowed, thereby addressing governance weaknesses arising from spatial inequality.

Second, from the perspective of resilience-network operation, there remains considerable potential to enhance the radiating and driving effects of core cities. Shanghai, Nanjing, Suzhou, Wuxi, Changzhou, and other core network cities should establish institutionalized mechanisms for disaster-prevention technology transfer, coordinated allocation of emergency supplies, and experience sharing, thereby extending governance capacity to peripheral cities. Cities with relatively low network participation, such as Tongling and Zhoushan, should address deficiencies in flood-control and drainage infrastructure, actively connect with the collaborative networks of core cities, and strengthen both their node activity and their capacity to receive and utilize regional resources. In accordance with the block spillover structure, the supply functions of the existing net-spillover blocks should be stabilized, mutual assistance within the bidirectional-spillover block should be strengthened, and the net-beneficiary block should be encouraged to shift from passively receiving resources to actively participating in network development. Measures should also be taken to compensate for the lack of a broker block and the resulting gaps in cross-block resource transfer and coordination, thereby improving the overall efficiency of resource circulation throughout the network.

Third, the institutional design of cross-regional collaboration should account for the evolving effects of different drivers. On the one hand, the complementary incentives arising from disparities in urbanization levels, fiscal self-sufficiency, and public attention should be leveraged to overcome administrative barriers and promote the coordinated allocation of disaster-prevention funds and the sharing of emergency information. On the other hand, the positive role of geographical proximity should be fully utilized, while digital platforms should further amplify the coordination benefits associated with spatial proximity and support the establishment of remote collaborative dispatch systems. Given the gradual weakening of the effects of infrastructure disparities and institutional proximity, future governance should shift from aligning physical infrastructure and coordinating administrative hierarchies toward substantive joint prevention and collaborative governance based on complementary capabilities. This requires the establishment of unified standards for joint flood-risk prevention and control, coordinated cross-regional emergency-response plans, and mechanisms for sharing fiscal responsibilities across jurisdictions, thereby ensuring the long-term and effective operation of networked collaborative governance for urban flood resilience in the YRD.

5 Limitations and future studies

Although this study systematically examines the spatiotemporal evolution, network structure, and driving factors of urban flood resilience in the YRD, several limitations remain. Specifically, due to constraints in data availability and indicator measurement, the analysis is conducted at the prefecture-level city scale, which may obscure disparities in flood resilience and cross-regional interactions at finer spatial scales, such as districts, counties, and communities. Moreover, the selection of indicators may influence the measurement and interpretation of urban flood resilience, as the selected indicators may not fully capture certain dimensions of resilience, such as institutional adaptability, community participation, and social equity. Differences in indicator availability, measurement quality, and weighting methods may also affect the assessment results. In addition, the spatial association network is constructed using a modified gravity model, and therefore reflects potential intercity linkages rather than directly observed flows of emergency supplies, disaster information, personnel, or funds. Future research could obtain more detailed first-hand and flow-based data through field investigations, governmental emergency-response records, and digital-platform information; extend the analysis to finer spatial scales and different types of flood scenarios. Doing so would help reveal more precisely the formation and evolution mechanisms of urban flood-resilience networks and provide stronger theoretical and empirical support for differentiated, cross-regional flood-risk governance.

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Footnotes

Edited by: Kaipeng Hu, Yunnan University of Finance and Economics, China

Reviewed by: Yujia Chen, Tianjin University, China

Haoran Su, Harbin Institute of Technology, China