Evolution of Resilience Spatiotemporal Patterns and Spatial Correlation Networks in African Regional Economies

Abstract

This paper comprehensively utilizes the entropy-TOPSIS method, Lyapunov index, and kernel density estimation to measure the spatiotemporal evolution characteristics of regional economic resilience in 52 African countries (regions) from 2008 to 2019. It also examines the spatial network characteristics of regional economic resilience in each country (region) through gravity models and social network analysis. The findings reveal that: (1) Although the resilience of African regional economies fluctuates, it generally shows an improving trend. Traditional economic powers and regional giants such as Libya, Nigeria, South Africa, Egypt, Morocco, and Tunisia demonstrate outstanding performance in economic resilience. (2) In terms of scale resilience, the countries along the North African Mediterranean coast exhibit particularly prominent advantages. However, the overall performance of Africa in fiscal resilience and openness resilience tends to be weak. Industrial resilience is influenced by colonial legacies and tends to stabilize. (3) The differences in economic resilience values and the fluctuation trajectories of economic resilience levels converge. North African economies exhibit resilience far higher than the mean and other regions, while East, West, and Central Africa consistently perform below the mean in the long term. Southern Africa’s gap from the mean is relatively small, leading to a stalemate. The fluctuation amplitude of differences within each region varies. (4) The overall level of resilience in African regional economies has steadily improved, displaying a trend of polarization. There is evident spatial polarization in West Africa, with Southern Africa demonstrating a trend of multipolarity transitioning towards bipolarity. Conversely, North Africa strengthens its features of bipolar differentiation, while East and Central Africa exhibit tendencies towards multipolarity. (5) Despite some fluctuations in the spatial network of regional economic resilience around 2016, connections among African countries have become increasingly tight, gradually forming three major spatial correlation network clusters: the North African Mediterranean coast, the West–Central African Pan-Gulf of Guinea region, and the East–South African Rift Valley region. Nigeria holds a prominent position as a regional core. Zambia, Cameroon, and the Central African Republic have played certain regional core roles at different times. Nigeria and South Africa also demonstrate significant intermediary roles, while Zambia, Cameroon, and Burkina Faso act as bridges in different periods of network connections. Based on the characteristics of spatial correlation networks, African regions gradually form four major cohesive subgroups and eight sub-subgroups.

1. Introduction

As a collection of complex systems, regional economies do not follow a singular, balanced development path; instead, they are engaged in complex dynamic processes [1]. Throughout this journey, economies demonstrate their ability to withstand and adapt to crises, including unavoidable economic crises, natural disasters, population outflows, and other internal and external shocks. Scholars have drawn upon concepts from physics, engineering, and ecology to develop the concept of “regional economic resilience”. With the global economic situation declining and uncertainties in economic development increasing, the resilience of economies has once again become a focal point of attention for scholars both domestically and internationally. Currently, with ongoing regional conflicts and hot spot issues worldwide, Africa—as an important comprehensive strategic partner of China—is facing new challenges in its development. From the perspective of regional economic resilience, examining the current development status of African economies is undoubtedly of great significance for enhancing China’s ability to withstand risks in its investments in Africa, realizing high-quality development in Sino-African cooperation and promoting high-quality development in investments in Africa.

The theory of “regional economic resilience” has evolved primarily through three perspectives, undergoing two transformations. From the initial perspective of singular equilibrium to multiple equilibria. From the evolutionary perspective, each cognition has its own era background and application scenarios. Each revision and enhancement enriches the connotations and extensions of the resilience concept [2].

The perspective of singular equilibrium defines regional economic resilience as akin to engineering resilience based on the principles of mechanical motion in physical systems. It views resilience as the ability of an object to return to its initial state after being subjected to pressure [3].

Holling was the first to introduce this mechanical concept into the fields of ecology and engineering [4]. Since the 1970s, the cyclical nature of economic crises has led economists to gradually recognize the differences in the ability of different economies to resist economic shocks and recover. Economists such as Reggiani began to introduce the concept of resilience into the fields of regional economics and urban economics, suggesting that economies may deviate from their development paths under external shocks but that over time, regional development will converge back to its initial state [5].

The perspective of multiple equilibria builds upon the foundation of a singular equilibrium by introducing the concept of ecological resilience. Martin and others found that under external shocks, economies do not necessarily converge to a single equilibrium, and regional development does not exhibit a singular equilibrium; instead, it may lead to either the emergence of new stable states or collapse [6]. Hassink discovered that the trajectory of economic development is multiple rather than singular [7].

The perspective of evolution theory builds upon the foundation of multiple equilibria, further breaking away from constraints and proposing evolutionary resilience. It suggests that the development of economies is not about equilibrium but rather non-equilibrium and complexity. Martin argues that resilience is an inherent attribute of regions, independent of external shocks but correlated with external factors, and it varies over time and space [8]. Regions do not possess equilibrium states, nor do they converge towards them. Therefore, defining resilience by crisis states at specific time points lacks theoretical basis. Evolutionary resilience is defined as the ability of regions to continuously optimize internal elements to adapt to external environmental changes and sustain growth, which arises from the comprehensive interaction of internal and external factors and historical path dependence [9]. This historical path dependence is characterized by contingency, but transformations and adjustments entail significant threshold effects, which are related to industrial diversity, innovation atmosphere, and top-level design [10,11].

Based on different theoretical perspectives, scholars have conducted a series of empirical studies. From a global perspective, looking at cross-basin large-scale scenarios, the resilience of the sixteen Eastern European countries varies greatly under the current economic background. Industrial structure becomes a crucial factor determining resilience. However, European integration has a dual effect on resilience [12]. Therefore, whether the sixteen Eastern European countries should join the European Union and the top-level design after joining requires a balanced consideration between overintegration into the European industrial chain and reliance on European investment [12]. From the perspective of resilience across the entire European region, it is more influenced by historical path dependence, particularly in the manufacturing sector as well as in the construction, finance, and non-market service sectors. Therefore, improving the rationality of industrial structure and enhancing the stability of production structure are important ways to enhance regional resilience and mitigate the impact of future economic downturns [13].

Focusing on the domestic perspective, Zhou Xia and colleagues constructed an economic resilience indicator system based on four dimensions: development-driven, pressure-sustained, resistance-released, and recovery-restructured. From the provincial level, they depicted the spatial evolution pattern and found that the spatial distribution of economic resilience across China’s provinces has shifted from “strong in the north, weak in the south” to “strong in the south, weak in the north”. This demonstrates a “east–central–northeast–west” stepwise effect, with the advantages of urban agglomerations becoming more prominent. Over time, the resilience level has shown a tendency toward dispersion, with absolute differences increasing and a growing trend toward unipolarity. Additionally, economic resilience and eco-efficiency exhibit a regionally differentiated pattern of coordinated evolution [14]. Jiang Zhengyun and colleagues used GDP value added as a proxy index for economic resilience to examine China’s provincial economic resilience over a long time scale. Their findings reveal that the temporal pattern of provincial economic resilience in China shows a dynamic “W-shaped” fluctuation with an upward trend. Spatially, the characteristics of imbalance are becoming increasingly pronounced [15]. Zhao Jianji and colleagues continue to use the GDP growth rate as a measure of economic resilience, focusing on small-scale units such as cities and counties. Their research concludes that the resilience levels in central and western China are higher than those in the eastern and northeastern regions, with continuous improvements in resilience. However, resource-based cities and old industrial cities exhibit a clear downward trend. Additionally, the study highlights that the influence of specialization and diversification on economic resilience varies significantly across regions during both the resistance and recovery phases [16]. Zhang Mingdou and colleagues, focusing on resistance and recovery pressures, adaptive adjustment, and innovative transformation capabilities, developed a multi-indicator system to assess urban economic resilience. They found that the economic resilience of cities within the Yangtze River Delta urban agglomeration has been steadily increasing, with highly resilient areas concentrated around provincial capitals. Moreover, there is a significant spillover effect between different spatial network regions of resilience [17]. The resilience economic indicator system, constructed based on resistance, recovery, and adaptability, reveals different measurement results when applied to the Central Triangle urban agglomeration compared to the Yangtze River Delta. The findings show a convergence of resilience and high-quality development levels, both trending upward. The number of regions with medium-high resilience has gradually increased, forming a pattern of “higher resilience in the southeast and lower resilience in the northwest” [18]. Throughout the dynamic evolution of the entire Yangtze River Economic Belt, the resistance and recovery components of resilience exhibit divergent development trajectories. Resistance shows an initial increase followed by a decline, while remaining at a generally high level. In contrast, recovery displays significant fluctuations. Factors such as diversification, related diversification, and regional innovation capacity play a crucial role in shaping these resilience dynamics [19]. Liu Yi and colleagues took a different approach by not using traditional GDP growth metrics to characterize economic resilience nor by establishing a multidimensional indicator system. Instead, they developed separate resilience metrics for exports, employment, consumption, and industry, focusing on the Guangdong–Hong Kong–Macau Greater Bay Area. Their findings reveal distinct resilience characteristics within the Bay Area, with significant variations in economic resilience among cities. These differences are closely related to the cities’ industrial economic structures and their integration into global production networks. Strategic coupling emerges as an effective means to explain these spatial disparities [20]. Scholars have also conducted research on regional economic resilience in areas such as the Yellow River Basin [21], Northeast China [22], and the Beijing–Tianjin–Hebei urban agglomeration [23,24], greatly enriching the materials for the study of regional economic resilience [25,26,27].

With increasing pressure from global economic downturns and growing uncertainty in economic development, the application scenarios of regional economic resilience theory have greatly expanded. However, there are still several shortcomings: Firstly, current research tends to focus on narrow aspects, with relatively few studies on the world geopolitical landscape and national resilience. However, given the imperative to serve the Belt and Road Initiative and promote China’s peaceful rise, a broad global perspective is urgently needed. Secondly, most studies primarily measure regional economic resilience based on static factors, often overlooking regional interconnectivity. When a region is impacted by external crises, it transmits through spatial correlation networks to other regions, forming a ripple effect.

This study draws on the spatial research methods of China’s regional economic resilience, focusing on 52 African countries (or regions). It conducts a comprehensive assessment of the economic resilience of these 52 African countries (or regions) by using a regional economic resilience indicator system combined with the entropy-weighted TOPSIS method. The Lyapunov exponent is applied to measure the spatial differences in Africa’s economic resilience, while kernel density estimation is used to analyze the temporal dynamics of resilience evolution. The gravity model and social network analysis are employed to examine the characteristics of Africa’s regional economic network from the perspective of economic resilience. The goal is to depict Africa’s regional economic resilience from multiple angles in terms of temporal and spatial scales, explore its spatiotemporal transition patterns, and uncover its underlying principles. On one hand, this study aims to contribute to the development of regional economic resilience research methods, and on the other hand, it seeks to enhance the macro-level understanding of Africa’s economy, providing foundational research support for future infrastructure investments and aid projects in Africa.

2. Materials and Methods

2.1. Measurement of Economic Resilience

Measurement methods for regional economic resilience mainly consist of constructing indicator systems and single indicator measurements [24]. Single-indicator measurement offers the advantage of conducting long-term analysis of economic resilience, but it suffers from weak explanatory power. On the other hand, indicator system measurement provides comprehensive coverage of indicators; however, it is often constrained by data availability, and the subjectivity of setting weights is frequently questioned.

To strike a balance between advantages and disadvantages, this study draws on the research findings of Song Yuchen et al. and constructs an indicator system for assessing resilience in the African region [25] (as shown in

Table 1. System of economic resilience indicators for the African region.

Primary Indicators	Secondary Indicators	Measurement Indicators	Unit of Measurement	Direction
Scale Resilience	Economic Size	GDP at Current market prices	Million US Dollars	Positive
	Asset Size	Gross Capital Formation	Million US Dollars	Positive
	Population Size	Economic Active Population	Thousands	Positive
	Consumer Market Size	Residential Consumer Expenditure	Million US Dollars	Positive
Fiscal Resilience	Government Revenue	General Budgetary Revenue	Million US Dollars	Positive
	Government Payment Ability	Government Fiscal Surplus	Million US Dollars	Positive
	Government Endogenous Debt Repayment Ability	Unpaid External Debt/GDP	%	Negative
	Government Exogenous Debt Repayment Ability	External Debt Service/Gross Exports	%	Negative
	Government Fiscal Self-Sufficiency Level	General Budgetary Revenue/Expenditure	%	Positive
	Government International Balance of Payments	Current (Transactions) Account Balance/GDP	%	Positive
		Trade Balance/GDP	%	Positive
Openness Resilience	Foreign Trade Dependence Ratio	Total Import and Export/GDP	%	Positive
	Foreign Capital Dependence Ratio	Foreign Direct Investment/GDP	%	Positive
	Official Aid Dependence Ratio	Government Development Assistance/GDP	%	Positive
Structural Resilience	Manufacturing Industry Index	Manufacturing Industry Output/GDP	%	Positive
	Mining and Energy Industry Index	Mining and Energy Industry Output/GDP	%	Negative

The data source is the African Statistical Yearbook, and the years covered in the study are 2008–2019.

). Specifically, this system includes four aspects: scale resilience, fiscal resilience, openness resilience, and structural resilience. GDP is a commonly used indicator to measure the scale of a regional economy. Gross capital formation consists of gross domestic fixed capital formation plus net changes in the level of inventories and is used to measure the current asset size of an economy. Economic active population refers to all individuals aged 16 and above who, within a given period, provide labor for various economic production and service activities. It is a commonly used indicator for measuring labor resources, and a strong base of economically active population is a key factor ensuring economic resilience. Residential consumer expenditure refers to the total spending by individuals and families on personal living expenses, as well as collective expenditures for individual consumption. It is an important indicator for measuring the consumption-driven capacity of an economy and its economic resilience. General budgetary revenue is an important source of government investment and a key indicator for measuring the fiscal strength of a government. Government fiscal surplus, which takes government expenditures into account, reflects the usual profitability of an economy. It serves as an important support for economic resilience. Unpaid external debt/GDP reflects a government’s ability to repay foreign debt using its own resources. External debt service/gross exports is an indicator used to measure an economy’s ability to repay its debt through export revenues. General budgetary revenue/expenditure reflects an economy’s current ability to be financially self-sufficient. Current (transactions) account balance/GDP and trade balance/GDP are crucial indicators of an economy’s short-term debt repayment capacity. They measure the economy’s ability to respond to economic crises. Total import and export/GDP, foreign direct investment/GDP, and government development assistance/GDP are indicators of the ability of trade, FDI, and ODA to generate self-sustaining economic growth. These indicators themselves exhibit a dual nature when measuring economic resilience. Considering that past crises in African economies have often been driven by endogenous factors, such as political coups, and that current crisis recovery largely depends on international aid, this analysis treats the degree of dependence on foreign trade, foreign investment, and official development assistance as positive indicators. Manufacturing industry output/GDP reflects the role of the manufacturing sector in economic development. A robust manufacturing system serves as a critical “ballast” for stabilizing economic growth. Mining and energy industry output/GDP is an important indicator for measuring an economy’s dependence on energy. A high proportion of mining and energy industries can link economic development to energy prices, making the economy highly volatile and prone to the “Dutch disease”, which significantly undermines regional economic resilience.

2.2. Entropy-Based TOPSIS

This study, drawing upon the research findings of Li Liangang, Wang Bing, and others, utilizes the entropy method to determine indicator weights, thereby mitigating the subjectivity inherent in weighting [25,28]. Following the normalization of each indicator, the entropy method is employed to ascertain the weights of the indicators. Subsequently, the technique for order of preference by similarity to ideal solution (TOPSIS) is employed to conduct an optimal proximity analysis of the resilience of African regional economies from 2008 to 2019. The combination of the entropy method and TOPSIS effectively reduces the subjective interference in indicator weighting, to some extent mitigating the subjectivity in determining the weights of the indicator system.

2.3. Lyapunov Index

This study, drawing on the research results of Fang Yi, Song Yuchen, and others, introduces the research methodology of complex systems theory into the measurement of regional economic resilience differences [27,28]. The Lyapunov index is primarily used to assess the stability of complex systems and can effectively reflect the average spatial distance dispersion. The calculation formula is as follows:

$$\widehat{\sigma }\left(X_t\right)=\sqrt{{\displaystyle \frac{1}{\left(N-1\right)H}}\sum _{k=t-h}^{t+h}\sum _{i=1}^N{\left(X_{i,k}-{\widehat{m}}_t\right)}^2}$$

(1)

$${\widehat{m}}_t={\displaystyle \frac{1}{NH}}\sum _{k=t-h}^{t+h}\sum _{i=1}^N{X}_{i,k}$$

(2)

$$H=2h+1$$

(3)

To ensure degrees of freedom, following Fang Yi et al., we set h = 1; $\widehat{\sigma }\left(X_t\right)$ represents the regional economic difference value at time t; $X_{i,k}$ denotes the level value of economic resilience measurement for African countries (regions). N represents the number of research units. t represents the specific year being measured.

2.4. Kernel Density Estimation

To further explore the dynamic evolution of economic resilience levels in African regions, this study employs kernel density estimation to analyze the distribution, shape, spread, and polarization trends of economic resilience development levels across different African countries (regions) [29].

$$f\left(x\right)={\displaystyle \frac{1}{Nh}}\sum _{i=1}^{N}K\left({\displaystyle \frac{X_i-x}{h}}\right)$$

(4)

$$K\left(x\right)={\displaystyle \frac{1}{\sqrt{2\pi }}}exp\left(-{\displaystyle \frac{x^2}{2}}\right)$$

(5)

In the equation, $f\left(\mathrm{x}\right)$ represents the probability density function of economic resilience, $K\left(·\right)$ denotes the Gaussian kernel function, and $K\left(x\right)$ represents the expression of the Gaussian kernel function. N represents the number of observations, h represents the bandwidth, $X_i$represents the sample observations, and x represents the mean of the observations.

2.5. Gravity Model

To elucidate the spatial correlation network status of economic resilience across African countries (regions), this study, referencing the work of Zhang Mingdou et al., constructs a spatial correlation matrix for economic resilience in the African region. The intensity of inter-country correlation is computed using the gravity model. To prevent weak economic correlations from affecting the overall distribution of the regional economic resilience network, a threshold f* (the mean of the removed outliers from the gravity matrix) is set for the inter-country economic connectivity matrix. This matrix is then transformed into a binary matrix using Equation (8) [30,31].

$$F_{ij}=K_{ij}{\displaystyle \frac{R_i·R_j}{D_{ij}^2}}$$

(6)

$$K_{ij}={\displaystyle \frac{R_i}{R_i+R_j}}$$

(7)

$$F(i,j)=\left\{\begin{array}{c}0f_{ij}<f^{*}\hfill \\ 1f_{ij}\ge f^{*}\hfill \end{array}\right.$$

(8)

In the equation, $F_{ij}$ represents the gravity level between country (region) i and j, R represents the regional economic resilience level of different countries (regions), $D_{ij}$ represents the geographical distance between two countries, and this study uses the Euclidean distance between the capitals of two countries. $K_{ij}$ represents the empirical coefficient [30].

2.6. Social Network Analysis (SNA)

A method of social network analysis (SNA) is a key method for studying the relationships among network members. It effectively reveals the structural connections between these members and their attribute characteristics [32]. In this study, the social network analysis software Ucinet 6.0 is utilized as the analytical tool. African countries (regions) are regarded as network nodes, and the connecting lines between nodes are used to represent the transmission effects of economic resilience between two countries.

(1) Overall network characteristics: This study employs network density (D), network connectivity (C), and the range of connection strengths (M) to measure the overall structural features of economic resilience in the African region. Network density is used to measure the degree of connectivity between nodes in the overall network; network connectivity reflects the stability or fragility of the overall regional network; and the range of connection strengths is used to characterize the balance of economic resilience connections within the network.

$$D={\displaystyle \frac{I}{N\left(N-1\right)}}$$

(9)

$$C=1-{\displaystyle \frac{V}{\left[N\right(N-1)/2]}}$$

(10)

$$M=F_{max}-F_{min}$$

(11)

I represent the actual number of relationships contained in the association network. N represents the total number of nodes in the overall network. V represents the number of regions in the network where connections cannot be established. $F_{max}\mathrm{a}\mathrm{n}\mathrm{d}{F}_{min}$ respectively represent the maximum and minimum values of regional resilience associations.

(2) Node Network Characteristics: This study utilizes degree centrality (DC) and betweenness centrality (BC) to depict the network structure characteristics of each node. Degree centrality measures the central position of a node in the network, with higher degree centrality indicating a more prominent central position of the node. Betweenness centrality reflects the intermediary role of a node in the overall network, with higher betweenness centrality indicating a more pronounced intermediary bridge effect.

$${DC}_i=K_i/(N-1)$$

(12)

$${BC}_i={\displaystyle \frac{2}{\left(N-1\right)(N-2)}}\sum _{s=1}^N\sum _{t=1}^N{\displaystyle \frac{{\delta }_{st}\left(i\right)}{{\delta }_{st}}}$$

(13)

In the equation, $K_i$ is the number of edges connected to node i. N − 1 is the maximum possible number of edges that node i can be connected to. ${\delta }_{st}$ is the number of shortest paths from node s to node t. ${\delta }_{st}\left(i\right)$ is the number of shortest paths from node s to node t that pass through node i.

(3) Cohesive Subgroup Analysis: Cohesive subgroups are a broad concept of actor subsets in social network analysis, where actors within this set have relatively strong, direct, close, frequent, or positive relationships. This indicator can reveal which countries (regions) in Africa have closer connections between nodes and the impact of this subgroup on the overall network.

2.7. Data Sources

Due to data availability limitations, this study excludes the Western Sahara region, South Sudan, and Somalia. The data mainly come from the African Statistical Yearbook and International Statistical Yearbook from 2009 to 2020 as well as national statistical yearbooks. Foreign direct investment data for Guinea-Bissau in 2018 is missing, and imputation was performed using adjacent data. For Mauritius, the manufacturing output data for 2012 is missing and was imputed using the average value. The original map in this article is sourced from the Map Technology Review Center of the Ministry of Natural Resources of China, and the regional classification follows the United Nations classification method.

3. Spatial–Temporal Patterns and Evolution of Regional Economic Resilience in Africa

3.1. Spatial–Temporal Patterns of Regional Economic Resilience in Africa

The regions in Africa with higher economic resilience are mainly concentrated in countries such as Libya, Kenya, the Democratic Republic of the Congo, Angola, Nigeria, South Africa, Egypt, Morocco, Tanzania, Sudan, and Tunisia. These regions are mostly economically developed areas or regional powers in the traditional sense, with developed economies bringing in substantial fiscal revenues and relatively well-established industrial structures, which to some extent enhance economic resilience. However, the economic resilience values of different countries fluctuate at the same time point, indicating regional differences in economic resilience levels between countries. Based on the mean economic resilience of the African region, approximately 12 countries consistently maintain a level above the mean. Among them, the proportion of high-resilience countries in North Africa, although initially high, has gradually decreased from 50% in 2008 to 27.3% in 2019; while the proportion of high-resilience countries in East and West Africa has shown an upward trend, increasing from 16.7% and 8.3% in 2008 to 27.3% and 18.2% in 2019, respectively (as shown in Figure 1a). The decline in economic resilience in North Africa is related to political unrest, from the 2011 Libyan Civil War to the “Jasmine Revolution” in Tunisia and the Egyptian Revolution. The Western-led “Arab Spring” political movement swept across North Africa, weakening economic resilience to some extent. Despite this decline, North Africa remains one of the most economically resilient regions in Africa. Overall, from 2008 to 2019, the economic resilience of the African region has shown an upward trend, despite fluctuations such as “growth–stagnation–decline–rebound”. The period from 2009 to 2013 witnessed steady growth in economic resilience; from 2013 to 2014, resilience remained almost unchanged, showing a stagnation status; from 2014 to 2017, economic resilience exhibited a declining trend; and from 2017 to 2019, regional economic resilience rebounded (as shown in Figure 1b). The economic resilience of North Africa is significantly higher than that of other regions in Africa, consistent with the analysis results showing a higher number of high-resilience countries in North Africa. East, West, and Central Africa have long been below the mean resilience value, while Southern Africa’s difference from the mean value is not significant, resulting in a stalemate.

To further explore the dynamic evolution of regional resilience in Africa across various sub-dimensions, this study has produced heatmaps depicting the resilience levels of each country and each sub-dimension (Figure 2). The horizontal axis represents the 52 countries (regions) in Africa, while the vertical axis represents the resilience level for each year. Darker shades indicate higher resilience levels, while lighter shades indicate lower levels.

According to Figure 2a, which represents the heatmap of the dynamic evolution of overall resilience among the 52 countries (regions) in Africa, it is evident that the overall regional resilience in Africa is steadily improving, with fluctuations between years but maintaining an average annual growth rate of 1.6%. There are significant differences in the extent of improvement among countries, consistent with the analysis results presented earlier. Following the economic crisis of 2008, African countries stabilized their economic fundamentals due to their abundant resources, leading to a steady overall increase in economic resilience. There is noticeable regional variation in the resilience of scale. Scale resilience is closely related to the size of the economy and is a concentrated reflection of the benefits of economic scale in the field of regional economic resilience. North African countries generally exhibit strong scale resilience, while regional powers like South Africa and Nigeria demonstrate remarkable scale resilience. Fiscal resilience is an important indicator reflecting the government’s ability to stabilize and drive economic development during crises. Fiscal resilience in Africa is somewhat weak, declining by 1.6% from 2008 to 2019, mainly due to the high debt levels in many African countries. However, economically developed countries such as Algeria, Egypt, Nigeria, and South Africa still exhibit respectable fiscal resilience due to their strong revenue generation capabilities. Openness resilience reflects the ability of foreign investment to impact the economy. Africa’s openness resilience has been weakened by international environmental shocks, declining by 22.1% from 2008 to 2019. Structural resilience represents the ability of industrial structure to influence regional economic resilience. There has been little change in structural resilience in Africa, tending towards stability overall. African countries’ industrial structures are heavily influenced by their former colonial rulers, with industries primarily focused on agriculture, energy, mining, and primary processing. Most countries participate in the industrial division of labor established by colonial powers, resulting in almost no complete industrial systems except for South Africa and some North African countries. Some countries are heavily dependent on the oil industry, suffering from the “Dutch disease”. For instance, Nigeria—Africa’s largest economy—derived 83% of its national revenue from the oil industry in 2018. Short-term improvements in industrial structure are challenging, hence the stability in structural resilience.

3.2. The Territorial Disparities of Economic Resilience in Africa

To further explore the regional disparities in economic resilience across Africa, this study utilizes the Lyapunov index to depict the dynamic evolution of economic resilience and internal disparities within the regions of Africa, including North Africa, East Africa, Southern Africa, West Africa, and Central Africa, with reference to the average economic resilience of the 52 countries (regions) in Africa.

The economic resilience in Africa demonstrates a fluctuating upward trend, and the differences in economic resilience values undergo a process of “initial increase, subsequent decrease, and then increase again”, showing a lag of 1–2 years compared to the overall trend. The peak of African regional economic resilience occurred in 2013–2014, while the peak in the differences in economic resilience values was reached in 2014–2015 (Figure 3a). In North Africa, the internal disparities exhibit a process of “steady growth, short-term decline, and then rise again”, with values significantly higher than the overall economic resilience differences in Africa, particularly in 2019, reaching 0.22, far exceeding other regions of Africa (Figure 3b). In East Africa, economic resilience generally remains below the resilience mean until it surpasses it in 2019. The internal disparities in East Africa experienced a turning point in 2010, showing a process of “decline, steady growth, and rapid growth” (Figure 3c). Southern Africa alternates between leading and lagging behind the resilience mean, consistently above the mean from 2008 to 2014, surpassed by the mean from 2015 to 2016, surpassing it again from 2016 to 2017, and then surpassed again by the mean in 2019. The internal disparities in Southern Africa showed fluctuations with turning points in 2010 and 2017, demonstrating a process of “increase, decrease, increase, and decrease” (Figure 3d). West Africa’s economic resilience remains below the mean, while its internal disparities experienced turning points in 2016 and 2018, showing a process of “long-term growth, rapid decline, and then rise again” (Figure 3e). Similarly, Central Africa’s economic resilience also remains below the mean, with internal disparities showing a process of “initial decrease followed by increase”, but with values significantly lower than other regions of Africa (Figure 3f).

3.3. The Temporal Evolution of Economic Resilience in the Africa

To further explore the spatiotemporal evolution patterns of economic resilience in African regions, this study employs the Matlab 2023a software to perform kernel density estimation on the economic resilience of the African region as a whole and its individual regions (as shown in Figure 4). The overall kernel density levels are plotted, and the analysis focuses on the mobility trends, polarization trends, distributional shapes, and extensiveness of the studied entities.

First, examining the distribution position, the central point of the kernel density function curve for overall economic resilience in Africa shows a rightward shift from 2008 to 2019. This indicates a steady improvement in the overall economic resilience level of the African region. Additionally, no significant leftward shift is observed in other regions of Africa, suggesting that there are no signs of marked economic resilience decline or weakening in these areas. Overall, both Africa as a whole and its individual regions exhibit stable to positive trends in economic resilience, aligning with the findings of the previous analysis.

Second, regarding the number of peaks, the kernel density function curve for overall regional economic resilience in Africa exhibits a unimodal structure with relatively steep peaks, indicating polarization characteristics during this period. West Africa shows an approximate high-low bimodal structure, highlighting significant regional economic resilience polarization, with a substantial distance between the main and secondary peaks, indicating pronounced spatial polarization within the region. South Africa demonstrates a distinct trimodal structure, with the first side peak gradually converging towards the main peak. North Africa shows a trend of transitioning from a unimodal to a bimodal structure, suggesting strengthening bipolar characteristics and increasing internal differentiation, consistent with earlier analyses. East and Central Africa display a trend from unimodal to bimodal to multimodal, indicating a trend towards multipolarization in economic resilience, with widening gaps in regional economic resilience development among countries. This trend reflects a significant “Matthew Effect”, corroborating the results of the Lyapunov exponent analysis.

Third, considering the main peak distribution, the height of the kernel density function curve for overall regional economic resilience in Africa has decreased, and its width has slightly broadened. This indicates an increase in the dispersion of economic resilience among the countries in the sample. The primary reason for this is the significant differences in economic size and industrial composition among African countries, resulting in diverse levels of economic resilience. North, East, and Central Africa exhibit trends consistent with the overall African region. However, Southern and Western Africa show no significant changes in the height and width of the main peak.

Finally, examining the distribution’s tail extension, the kernel density function curves for overall African regional economic resilience, as well as for Southern, Western, and Central Africa, exhibit right-tail elongation. This indicates the presence of some countries within these regions that have significantly stronger economic resilience compared to others. In contrast, Northern Africa does not show a pronounced right-tail elongation.

4. Spatial Correlation Network of Economic Resilience in Africa

4.1. Overall Network Structural Characteristics

Based on the gravity model, this study calculates the regional economic resilience gravity values among 52 African countries (regions) and evaluates the spatial network structure characteristics of African regional economic resilience (

Table 2. Characterizing the spatial network structure of economic resilience in the African region.

Indicator	2008	2012	2016	2019
Effective Network Connectivity	0.634	0.887	0.815	0.851
Total Number of Effective Connections	99	125	120	144
Network Density	0.075	0.094	0.091	0.109
Mean Connection Strength	1.92	2.31	2.11	3.12
Range of Connection Strength	2250.75	886.42	1605.87	907.03

).

A network association degree closer to 1 indicates higher accessibility of the spatial network, greater participation of network nodes, and higher overall network stability. In 2008, the effective network association degree was only 0.634, which increased to 0.887 in 2012. It experienced a slight decline in 2016, and then rose again to 0.851 in 2019. Concurrently, the total number of effective connection lines was only 99 in 2008, increased to 125 in 2012, slightly decreased to 120 in 2016, and reached its highest at 144 in 2019. Correspondingly, the overall network density of regional economic resilience increased from 0.075 to 0.109, indicating that despite minor fluctuations around 2016, the trend of increasingly tighter connections among African countries persisted.

Further analysis of the connection strength of economic resilience among countries shows that in 2008, it was only 1.92, which rose to 2.31 in 2012, declined slightly in 2016, and reached 3.12 again in 2019, demonstrating a significant enhancement in the level of overall economic resilience connections within the African region. This indicates that smaller countries, such as Liberia, Côte d’Ivoire, and the Central African Republic, have gradually participated in the resilience network. While the level of network connections has improved, the range of connection strength has fluctuated significantly without a clear trend, indicating that polarization within the network connections is not prominent.

To comprehensively identify the spatial network of economic resilience in Africa, this study utilized NetDraw and ArcGIS to create spatial network maps of African regional economic resilience for the years 2008, 2012, 2016, and 2019. Additionally, the top 50% of networks in terms of connection strength were selected as the backbone network, and spatial backbone network maps of African regional economic resilience for the years 2008, 2012, 2016, and 2019 were generated (Figure 5 and Figure 6).

It can be observed that the spatial network nodes of African regional economic resilience evolved from being relatively sparse in 2008 to becoming closely interconnected by 2019, consistent with the trends reflected in network density and network connectivity. Spatially, the 2008 economic resilience spatial network was concentrated in three regions: the North African Mediterranean coast, the West African–Central African pan-Guinea Gulf region, and the East African–Southern African Rift Valley countries. In 2012, the connections within these three regional areas significantly strengthened. By 2016, the connections between the Rift Valley countries and the Guinea Gulf region countries had become increasingly tight. In 2019, the three regions gradually merged into an integrated whole, with the Central African Republic playing a crucial linking role.

From the backbone network perspective, the roles of Nigeria, Algeria, South Africa, and Ethiopia have become increasingly prominent, establishing themselves as core nodes within their respective regions. In the West Africa–Central Africa Guinea Gulf region, Nigeria serves as the core node. In 2008, it had backbone connections with surrounding countries, and after 2012, its connections with southeastern Angola, Equatorial Guinea, the Democratic Republic of the Congo, and the Republic of the Congo became more pronounced. On the North African Mediterranean coast, Libya was initially the core node in 2008, connected to Nigeria. However, Algeria gradually replaced Libya as the new core node. In the East Africa–Southern Africa Rift Valley, Ethiopia and South Africa formed a dual-core network, with Kenya and Tanzania also steadily rising in their network positions.

4.2. Individual Network Analysis

To further investigate the roles of individual nodes within the network, this study employs the Network/Centrality and Network/Betweenness functions in Ucinet 6.0 to calculate the degree centrality and betweenness centrality of each node for the years 2008, 2012, 2016, and 2019. Additionally, spatial interpolation analysis using ordinary Kriging in ArcGIS 10.2 was conducted, resulting in the distribution maps of degree centrality (Figure 7) and betweenness centrality (Figure 8) for African regional resilience from 2008 to 2016.

4.2.1. Degree Centrality

According to Figure 7, the degree centrality of African countries in 2008 was generally low, with significant regional differences. The northwest region of Africa and the southeastern coast had the lowest degree centrality. By 2012, the degree centrality had significantly increased compared to 2008, indicating a substantial improvement in the tightness of network connections between 2008 and 2012. Nigeria and Zambia emerged as high points in degree centrality, becoming important regional cores, radiating influence respectively to the Guinea Gulf region and southern African countries. In 2016, the degree centrality saw a modest increase compared to 2012, with Nigeria maintaining a high degree of centrality and Cameroon emerging as a new high point. By 2019, the degree centrality had risen sharply again, with Nigeria, Cameroon, the Central African Republic, and Ethiopia gradually forming a connected area and South Africa’s degree centrality also becoming more prominent.

4.2.2. Betweenness Centrality

According to Figure 8, in 2008, the high points of betweenness centrality were primarily located near Guinea, Nigeria, and South Africa, indicating that the overall resilience of the African regional network heavily relied on these three areas, with clear regional imbalances. By 2012, South Africa’s bridging role had gradually been taken over by Zambia, which became a crucial hub connecting the northern and southern Rift Valley countries, while Nigeria remained a high point. In 2016, new high points emerged around Cameroon and Burkina Faso, forming a contiguous high-point area around Nigeria, including Cameroon, Côte d’Ivoire, and Burkina Faso. By 2019, betweenness centrality once again concentrated on Nigeria and the Central African Republic, with South Africa and Côte d’Ivoire also standing out as significant second-tier nodes. This indicates that these regions hold a dominant position in the spatial network of Africa’s economic resilience. The development of regional resilience is highly dependent on their intermediary roles, leading to an unbalanced and unstable economic resilience network. Regional powers still play a crucial role in the spatial network of regional resilience.

4.3. Block Modeling Analysis

Using Ucinet-Concor, a two-level clustering analysis was conducted on the 52 African countries (regions) from three perspectives [32,33,34]. Based on the agglomerative subgroup dendrogram, we plotted the first and second clustering diagrams of African regional economic resilience (Figure 9a,b) to further investigate the presence of “small groups” within the African resilience network. The analysis measures the degree of connectivity among the 52 countries (regions) and explores the coordination of regional resilience between these countries. The results indicate that (1) North African Mediterranean countries such as Egypt, Sudan, and Libya, along with East African countries like Ethiopia, Kenya, and Tanzania, form a cohesive subgroup. This subgroup is further divided by Sudan into two subgroups: the North African Mediterranean countries and the Sudan–East African countries; (2) the entire Gulf of Guinea region constitutes a cohesive subgroup, including northern Niger and southern Angola. This subgroup is further split by Nigeria into two subgroups: the northern Gulf of Guinea countries and the eastern Gulf of Guinea countries; (3) the entire Southern Africa region forms a subgroup, which is then divided by Botswana and Zimbabwe into two subgroups: the southeastern coastal countries of Africa and the South African interior and southwestern coastal countries; (4) the western coastal countries of West Africa, along with Mali, the Republic of the Congo, and Madagascar, form a cohesive subgroup. This subgroup is further split into the Mauritania–Sierra Leone–Cape Verde cohesive subgroup and the Mali–Guinea–Democratic Republic of the Congo–Madagascar cohesive subgroup.

5. Conclusions and Discussion

5.1. Conclusions

Regional economic resilience has become a significant theoretical concept in contemporary academic discussions on sustainable regional economic development under crisis conditions [35]. This paper uses 52 African countries (regions) as the empirical area, employing the entropy-weighted TOPSIS method to measure regional economic resilience, and utilizing the Lyapunov index and kernel density function to depict the spatial and temporal evolution trends and differences in economic resilience. Based on this, the gravity model and social network analysis methods are applied to explore the characteristics of the spatial correlation network of economic resilience, aiming to more comprehensively reflect the spatiotemporal characteristics of African regional economic resilience. The main conclusions are as follows:

(1) Overall, although African regional economic resilience has experienced fluctuations, it has generally shown a steady improvement. Traditional economic powerhouses and regional powers continue to perform well in terms of economic resilience. Geographically, North Africa’s economic resilience is significantly higher than the average and other regions. East Africa, West Africa, and Central Africa have long been below the average, while Southern Africa remains close to the average, with little difference. Despite being influenced by political factors, North Africa’s regional economic resilience has shown some decline but still stands out prominently.

(2) From the perspective of resilience sub-dimensions, North African countries and regional powers exhibit outstanding advantages in terms of scale resilience. Due to high debt levels and the impact of the international environment, the entire continent of Africa generally shows weak performance in fiscal resilience and openness resilience. Industrial resilience, influenced by colonial history, is unlikely to see significant short-term improvements and tends to remain stable.

(3) In terms of regional differences, the fluctuation of economic resilience differences shows a 1–2-year lag but follows a similar trend to the overall economic resilience. North Africa’s internal economic resilience and its regional difference values are higher than the average and other regions. East Africa’s economic resilience is generally below the resilience average, with difference values showing a “decline–steady growth–rapid growth” process, using 2010 as a turning point. South Africa’s regional economic resilience is on par with the average, and its difference values fluctuate between “rise–fall–rise–fall”. West Africa’s economic resilience is consistently below the average, with difference values showing a “long–term growth–rapid decline–rebound” pattern, with turning points in 2016 and 2018. Central Africa’s economic resilience has been below the average for a long time, and the absolute values of its differences are significantly smaller than those of other regions.

(4) In terms of spatiotemporal evolution patterns, the overall level of economic resilience in Africa has steadily improved and shows a polarization trend. Within West Africa, there is a clear spatial polarization of economic resilience. South Africa is transitioning from a multipolar to a bipolar trend, while North Africa is strengthening its bipolar characteristics. East Africa and Central Africa exhibit multipolarization, with increasing disparities in regional economic resilience development between countries, making the “Matthew effect” increasingly apparent.

(5) From the perspective of spatial association network characteristics, although there were minor fluctuations in the spatial resilience network among countries around 2016, the connections between countries have become increasingly tighter, with small and medium-sized countries gradually participating in the resilience network. The three major spatial association network concentration areas are the North African Mediterranean coast, the West Africa–Central Africa Gulf of Guinea region, and the East Africa–Southern Africa Rift Valley countries. Within these regions, the connections between countries have significantly strengthened, and through the Central African Republic as a hub, they are gradually integrating into a cohesive whole. Regional powers like Nigeria, Algeria, South Africa, and Ethiopia play crucial roles in the network, becoming core nodes in their respective sub-regional networks. The status of countries such as Kenya and Tanzania is also rising.

Regarding the roles of nodes in the network, Nigeria has consistently been a key core node in the Gulf of Guinea region, radiating influence outward. Zambia, Cameroon, and the Central African Republic have emerged at different times, each playing a certain core role. Nigeria and South Africa have consistently held prominent intermediary roles in the network, while Zambia, Cameroon, and Burkina Faso have played significant bridging roles in the network associations at different times. The development of the entire network’s resilience still heavily relies on the intermediary roles of major powers, and the economic resilience association network remains notably imbalanced and unstable. Based on the node spatial association network characteristics, the African region is divided into four major cohesive subgroups and eight sub-subgroups, with regional powers playing pivotal roles within each cohesive subgroup.

5.2. Discussion

The flow of regional economic factors exhibits both risk-aversion and economic rationality. In times of economic crises, there is a tendency for economic factors to move from regions with lower resilience to those with higher resilience. Regions with stronger economic resilience exert a “siphon effect” on surrounding areas, leading to the formation of interconnected networks. Spatial correlation networks based on economic resilience, to some extent, reflect the characteristics of regional economic networks. The purpose of employing spatial correlation network analysis is to examine the position and role of each node in the network from the perspective of economic resilience. This study focuses on 52 African countries (or regions) to explore the spatial correlation network of regional economic resilience in Africa, thereby examining the characteristics of Africa’s regional economic network through the lens of economic resilience.

Africa, as an important strategic partner of China, holds a crucial position in the Belt and Road Initiative (BRI). The past 20 years have witnessed rapid development in Africa. Against the backdrop of global economic downturns, exploring the issue of Africa’s economic resilience serves two purposes: on one hand, it reflects on the economic resilience challenges faced by rapidly developing economies during their growth processes; on the other hand, it contributes to the refinement of theoretical research methods in regional economic resilience. The risks and shocks faced by regions are diverse, and the factors influencing the spatial layout of regional economic resilience are also multifaceted [36,37,38,39,40]. Scholars have explored the factors affecting the economic resilience of African countries. For instance, the economic resilience of Sub-Saharan African economies largely depends on improvements in political governance, fiscal sustainability, and external balance [41]. In Southern Africa, however, regional economic resilience is less sensitive to population size, infrastructure development, and building density [42]. This paper has certain limitations: first, due to the lack of commonly used indicators such as business environment, national policy support, and total fixed asset investment to measure government management capacity, as well as the absence of statistical data on urban unemployment rates and educational attainment of the workforce, and incomplete data on indicators measuring technological innovation levels, such as patents per capita, data availability has limited the study of influencing factors. This paper primarily reveals the historical and current status of Africa’s regional economic resilience, and further research on influencing factors is warranted as statistical data improves. Second, the specific impacts of different external shocks, such as the European debt crisis and the COVID-19 pandemic, on Africa’s economic resilience are unique and merit further exploration and refinement by economic geographers in future studies.