Mapping Financial Connections: Market Integration in Emerging Economies through Graph Theory

Abstract

In this study, we explore the financial and economic integration of BRICS nations (Brazil, Russia, India, China, and South Africa) and key emerging economies (Egypt, Saudi Arabia, and the UAE) using graph theory, aiming to map intersectoral connections and their impact on financial stability and market risk. The research addresses a critical gap in the literature; while political and economic linkages between nations have been widely studied, the specific connectivity between sectors within these economies remains underexplored. Our methodology utilizes eigenvector centrality and Euclidean distance to construct a comprehensive network of 106 publicly listed firms from 2013 to 2022, across sectors such as energy, telecommunications, retail, and technology. The primary hypothesis is that sectors with higher centrality scores—indicative of their interconnectedness within the broader financial network—demonstrate greater resilience to market volatility and contribute disproportionately to sectoral profitability. The analysis yielded several key insights. For instance, BHARTI AIRTEL LIMITED in telecommunications exhibited an eigenvector centrality score of 0.9615, positioning it as a critical node in maintaining sectoral stability, while AMBEV SA in the retail sector, with a centrality score of 0.9938, emerged as a pivotal player influencing both profitability and risk. Sectors led by companies with high centrality showed a 20% increase in risk-adjusted returns compared to less connected entities, supporting the hypothesis that central firms act as stabilizers in fluctuating market conditions. The findings underscore the practical implications for policymakers and investors alike. Understanding the structure of these networks allows for more informed decision making in terms of investment strategies and macroeconomic policy. By identifying the central entities within these economic systems, both policymakers and investors can target their efforts more effectively, either to support growth initiatives or to mitigate systemic risks. This study advances the discourse on emerging market integration by providing a quantitative framework to analyze intersectoral connections, offering critical insights into how sectoral dynamics in emerging economies influence global financial trends.

1. Introduction

In the dynamic landscape of the global economy, the BRICS nations (Brazil, Russia, India, China, and South Africa), along with emerging economies such as Egypt, Saudi Arabia, and the United Arab Emirates, are reshaping the paradigms of commercial and financial integration. These economies represent a burgeoning force that is challenging traditional Western-centric economic norms and redefining the dynamics of global economic growth.

The BRICS, collectively accounting for approximately 42% of the world’s population and about 23% of global GDP, have achieved significant economic growth over the past few decades. This group of countries has established a new model of economic and political cooperation that challenges the hegemony of developed economies. Their influence spans various domains, from international politics to trade and investment, cementing their role as key players in the global economy (Stojković and Milosavljević 2023).

The importance of the BRICS in global economic development lies in their ability to mobilize substantial resources and generate economic growth both regionally and globally. These countries have created institutions such as the New Development Bank (NDB) and the Contingent Reserve Arrangement (CRA), which aim to provide financial alternatives to those offered by Western institutions like the World Bank and the International Monetary Fund (Garas et al. 2010). These initiatives not only strengthen their financial autonomy but also promote sustainable development and South–South cooperation.

The increasing economic interdependence among nations, particularly within emerging markets, presents complex challenges for understanding the structural dynamics of financial integration. This study addresses a key research problem; while much attention has been paid to the political and macroeconomic ties between countries, the sectoral connections that underpin these relationships are less explored. Specifically, we seek to understand how financial interconnections between sectors within BRICS nations and key emerging economies influence market stability and risk.

Previous research has broadly addressed the macroeconomic and political dimensions of integration between emerging economies (Humphrey and Messner 2006; Stojković and Milosavljević 2023), but there is a notable gap in the literature when it comes to mapping these relationships at the sectoral level. Herein lies the contribution of this study—by applying graph theory, specifically eigenvector centrality, we aim to provide a more detailed analysis of how sectors within emerging economies are interconnected and how these connections affect broader market dynamics such as profitability, volatility, and risk mitigation.

This study is motivated by the need to understand the innovative economic and financial integration model exemplified by the BRICS consortium and its associated emerging economies. Unlike traditional economic alliances, the BRICS consortium represents a paradigm characterized by diverse yet rapidly expanding economies, offering new perspectives on global economic strategies and necessitating a thorough exploration of their unique dynamics (Stojković and Milosavljević 2023). This phenomenon has garnered substantial academic interest and policy deliberation due to its potential to significantly influence global economic trends and financial stability (Badunenko and Romero-Ávila 2013).

This study distinguishes itself from prior research through the comprehensive application of graph theory, particularly eigenvector centrality, to analyze the structural dynamics of these emerging markets. Previous studies, such as those by Wang et al. (2024) have employed graph theory to a limited extent, often focusing on individual market behaviors rather than the interconnectedness and collective influence of these economies. By integrating a broader set of emerging economies and examining their collective impact on global economic stability and growth, this study provides a holistic view of economic integration and introduces innovative methodologies for analyzing economic interdependencies and market behaviors.

Graph theory offers a powerful framework for analyzing the complex interdependencies that exist between sectors. By modeling the financial markets as networks, this approach allows us to identify key sectors that act as stabilizers within the system. Eigenvector centrality—a measure of a sector’s influence based not only on its direct connections but also on the centrality of the sectors to which it is connected—serves as the primary tool for quantifying this influence. For example, a sector with high centrality can be a major driver of stability, shaping the overall resilience of the economy to external shocks.

The central research problem addressed in this study is the need to comprehend the intricate structural dynamics and influence of the BRICS nations and their associated emerging economies within the global financial system. This issue is critically important because these nations are rapidly emerging as central players in the global economy, impacting not only their regional markets but also having significant implications for global economic trends and stability (Obstfeld 1998; Rogoff 2002). Understanding these dynamics is essential for policymakers, investors, and analysts who must navigate the complexities of an increasingly interconnected global economy.

The practical relevance of this study cannot be overstated. For investors, understanding which sectors are most interconnected offers a new lens for identifying risk-adjusted investment opportunities. Policymakers, too, can use these insights to design more targeted economic policies that enhance sectoral resilience and mitigate systemic risk. For example, sectors led by highly central firms demonstrated a 20% increase in risk-adjusted returns, offering concrete evidence of the value of network centrality in financial strategy.

In sum, this research contributes to the field by (1) advancing the application of graph theory to the study of financial integration in emerging markets, (2) demonstrating the empirical relationship between eigenvector centrality and sectoral stability, and (3) providing a practical framework for both policymakers and investors to navigate the complex dynamics of financial networks.

Current solutions in the literature provide partial insights into the economic relationships within these emerging markets. For example, the application of eigenvector centrality in graph theory, as highlighted by Wang et al. (2024) offers a nuanced understanding of economic relationships and dependencies. However, these studies often lack a comprehensive analysis of the risks associated with integration and the policy implications necessary to mitigate these risks (Mamman et al. 2023). While some studies discuss the economic stability and growth potential fostered by integration, they also highlight significant drawbacks such as exposure to global financial volatility and policy spillovers (Liang et al. 2023). These issues underscore the necessity for more strategic macroeconomic policymaking that can leverage the benefits of integration while addressing its inherent risks.

This study aims to fill the gap in the existing literature by providing a detailed and comprehensive analysis of the economic relationships and dependencies within these emerging markets. By identifying key nodes—pivotal countries or corporations—that significantly influence the economic trajectory of the entire network, this research underscores the critical role of strategic policymaking in fostering economic stability and growth. The findings of this study are expected to contribute to the ongoing dialogue on the integration of these economies into the global financial system, offering valuable insights for policymakers and stakeholders involved in international finance and trade.

In summary, the commercial and financial integration of BRICS and candidate countries signifies a critical juncture in the global economic narrative. This integration, analyzed through graph theory, provides valuable insights into emerging market dynamics. It highlights the necessity for a sophisticated understanding of these complexities by policymakers, investors, and analysts navigating this intricate and continuously evolving economic landscape. This study not only advances academic discourse on global economic integration but also offers practical recommendations for enhancing economic stability and growth in the face of increasing interconnectivity.

2. Literature Review

The integration of BRICS nations and other emerging economies into the global financial system has garnered extensive scholarly attention. This literature review aims to highlight the most pertinent studies, elucidate their contributions, and demonstrate how this research advances the discourse on economic and financial integration.

The BRICS consortium has been conceptualized as a unique model of economic coalition distinct from traditional Western-centric economic alliances. Stojković and Milosavljević (2023) delineate the BRICS consortium as a paradigm shift, characterized by its diverse yet rapidly expanding economies that challenge the conventional norms of economic development and integration. Similarly, Humphrey and Messner (2006) discuss the evolving role of emerging economies in reshaping global economic governance. This coalition signifies a departure from established economic models by fostering a multi-polar global economic landscape. This study builds on their foundational work by extending the analysis to include emerging candidates such as Egypt, Saudi Arabia, and the UAE, thereby broadening the scope of economic integration beyond the BRICS nations.

Graph theory has been increasingly utilized to analyze the structural dynamics of financial markets. Wang et al. (2024) employed eigenvector centrality to understand the interconnectedness within emerging markets, identifying pivotal nodes that exert significant influence over the economic network. This approach offers a sophisticated method for mapping economic relationships and dependencies. Additionally, Garas et al. (2010) utilized network analysis to study systemic risk in financial networks, highlighting the critical nodes that contribute to financial stability. However, their analysis was limited to individual market behaviors. The present study expands this methodology by applying graph theory across multiple emerging economies, thus providing a more comprehensive understanding of global financial integration.

The nexus between economic integration and stability has been a focal point of recent research. Mamman et al. (2023) investigated how economic integration can foster stability and growth but also highlighted the concomitant risks of exposure to global financial volatility and policy spillovers. Similarly, Badunenko and Romero-Ávila (2013) examined the implications of financial integration for emerging markets, identifying both opportunities and risks. Their findings underscore the necessity of strategic macroeconomic policymaking to mitigate these risks. This study corroborates their findings and further explores the policy implications of economic integration, emphasizing the role of sophisticated risk management strategies.

Sectoral interconnectedness is a crucial indicator of financial health and economic stability. Khan et al. (2022) and Hoque et al. (2023) analyzed the interlinkages within technology and energy sectors, demonstrating how sectoral integration can enhance economic resilience. Lee and McKibbin (2018) also highlighted the importance of sectoral linkages in the context of financial crises, suggesting that stronger intersectoral ties can mitigate adverse effects. Their research indicated that sectors with higher degrees of interconnectedness tend to exhibit greater stability and robustness. This study extends their analysis by incorporating additional sectors such as retail, industry, and mining, providing a more holistic view of sectoral dynamics within emerging markets.

The role of multinational corporations (MNCs) in shaping global economic trends has been well documented. Mirza et al. (2023) examined the influence of MNCs from BRICS and candidate countries, highlighting their impact on both domestic and international markets. Osei and Kim (2023) further analyzed the growth effects of foreign direct investment facilitated by MNCs. Dunning and Lundan (2008) provided a comprehensive framework for understanding the strategies of MNCs in the global economy. This study integrates these perspectives, analyzing how MNCs contribute to the economic network and influence global market dynamics through their strategic operations and investments.

The integration of emerging markets is fraught with challenges. Liang et al. (2023) discussed the volatility and risks associated with natural resource dependency in emerging economies, while Mirza et al. (2023) addressed the broader challenges of integrating these economies into the global financial system. Obstfeld (1998) and Rogoff (2002) also examined the macroeconomic implications of financial globalization, emphasizing the need for robust policy frameworks to manage the associated risks. These challenges include exposure to financial shocks, the need for effective regulatory frameworks, and the strategic navigation of global economic policies. This research addresses these issues by providing in-depth analysis and proposing strategic responses to mitigate these risks. See

Table 1. Summary table: contributions of the literature vs. present study.

Study	Focus	Methodology	Findings	Innovation in Present Study
Humphrey and Messner (2006)	Emerging economies in global governance	Descriptive Analysis	Emerging economies are reshaping global economic governance	Explores the strategic aspirations of BRICS and emerging candidates
Wang et al. (2024)	Structural dynamics in emerging markets	Graph Theory	Identified key nodes influencing economic trajectory	Applies graph theory to multiple emerging economies for holistic analysis
Garas et al. (2010)	Systemic risk in financial networks	Network Analysis	Critical nodes contribute to financial stability	Extends network analysis to broader economic integration
Mamman et al. (2023)	Economic stability and growth potential	Empirical Analysis	Highlights risks of global financial volatility and need for strategic policymaking	Comprehensive risk analysis and policy recommendations
Badunenko and Romero-Ávila (2013)	Financial integration in emerging markets	Empirical Analysis	Identifies opportunities and risks of financial integration	Provides detailed policy implications and risk management strategies
Khan et al. (2022); Hoque et al. (2023)	Sectoral interconnectedness and financial health	Sectoral Analysis	Sectoral integration linked to financial stability	Detailed sectoral analysis using advanced econometric methods
(Lee and McKibbin 2018)	Sectoral linkages during financial crises	Sectoral Analysis	Stronger intersectoral ties mitigate adverse effects of financial crises	Incorporates additional sectors and broader market dynamics
Mirza et al. (2023)	Role of multinational corporations	Case Studies	Influence of MNCs in shaping global economic trends	Integrates MNCs’ role in broader economic network analysis
Dunning and Lundan (2008)	Strategies of multinational corporations	Theoretical Framework	Comprehensive framework for understanding MNC strategies	Analyzes strategic operations and investments of MNCs in emerging economies
Liang et al. (2023); Mirza et al. (2023)	Challenges of market integration	Empirical and Descriptive Analysis	Discusses exposure to financial shocks and policymaking challenges	In-depth analysis of integration challenges and strategic responses
Obstfeld (1998); Rogoff (2002)	Macroeconomic implications of financial globalization	Empirical Analysis	Need for robust policy frameworks to manage globalization risks	Proposes strategic navigation of global economic policies
Stojković and Milosavljević (2023)	BRICS consortium as an economic model	Descriptive Analysis	Diverse, rapidly expanding economies challenge conventional norms	Expands on coalition model by integrating broader set of emerging economies

, which compares the main insights from the literature with the findings and advancements presented in this paper.

3. Methodology

3.1. Hypothesis and Predictions

In recent decades, the global economic landscape has witnessed a paradigm shift, with emerging economies playing an increasingly significant role. This review explores the integration of these economies into the global framework, particularly examining the BRICS and candidate countries.

The application of graph theory, particularly eigenvector centrality, has proven invaluable in understanding economic interconnectivity. Bertsche et al. (2022) identified key nodes within the economic network of the BRICS, revealing how certain countries or corporations act as central influencers. This approach is bolstered by the work of Dai (2023), who analyzed how these structural connections affect regional economic stability. Hong (2023) employed advanced graph theory models to map the global influence of these emerging economies.

The integration of countries such as Egypt, Saudi Arabia, and the UAE adds a layer of complexity to the global economic network. Arapova and Lissovolik (2022) discuss how these economies are using their integration to propel their economic development and strengthen their position in the global market. Tripathy (2022) provides an in-depth view of how these countries are navigating the integration process, leveraging their strategic positions and resources.

The integration of emerging markets carries significant implications for global macroeconomic policy. Khan et al. (2022) and Mamman et al. (2023) argue that this integration requires a reevaluation and adaptation of international economic policies to capitalize on growth opportunities and manage associated risks.

Hoque et al. (2023) emphasize the need for flexible policies that can respond to the changing dynamics of the global market.

Sectoral interconnectedness within these emerging economies is a key indicator of their financial health and economic stability. Khan et al. (2022) highlighted how sectoral integration, especially in technology and energy, is linked to the overall financial health of economies. Hoque et al. (2023) delved deeper into this discussion, exploring the impact of sectoral interconnectedness on economic stability.

Multinational corporations play a crucial role in the economic integration process. Mirza et al. (2023) examined how MNCs from the BRICS and candidate countries are influencing both their domestic markets and the international economic landscape. Osei and Kim (2023) and Rath et al. (2023). analyzed the role of these corporations in shaping global economic trends.

Convergence in corporate governance is a key area of change and alignment with global standards. Oliveira et al. (2022) compared governance practices in the BRICS, noting a trend toward adopting practices of transparency and efficiency.

The challenges associated with integrating these emerging markets are significant. Liang et al. (2023) discussed how this integration, while offering growth opportunities, also exposes economies to global financial shocks. Mirza et al. (2023) addressed how these dynamics present both challenges and opportunities for policymakers and investors.

3.2. Study Predictions

Hypothesis 1.

Sectors with higher eigenvector centrality exhibit greater stability and resilience to market volatility.

Operationalization: Stability is quantified as the volatility of returns (standard deviation of sectoral returns), while eigenvector centrality measures sectoral importance within the financial network.

Hypothesis 2.

A dispersed centrality distribution within a sector correlates with higher innovation capacity.

Operationalization: Centrality dispersion is calculated as the standard deviation of centrality scores, while innovation is proxied by sectoral R&D spending and growth rates.

Hypothesis 3.

High-centrality sectors exert significant influence on global market dynamics.

Operationalization: Global influence is assessed through the correlation of sectoral returns with global indices, with eigenvector centrality capturing the sector’s systemic importance.

3.3. Sample, Variables Studied, and Descriptive Statistics

3.3.1. Sample

Our dataset consists of 106 publicly listed companies across eight countries, with financial data spanning from 2013 to 2022. These data were sourced from Bloomberg and include key financial performance indicators, sectoral returns, and market capitalization. The following steps were taken to ensure data quality:

Data Cleaning: We removed outliers and inconsistencies through Winsorization to cap extreme values and ensure robust statistical analysis.

Sectoral Standardization: To facilitate intersectoral comparison, all financial metrics were normalized by sector averages.

3.3.2. Variables Studied

The choice of financial indicators was closely aligned with our research objectives of measuring profitability and risk:

Profitability indicators: ROA (Return on Assets), ROE (Return on Equity), and Sales Ratio were chosen to capture operational efficiency.

Risk indicators: The Debt Ratio, Working Capital, and Accounts Receivable Turnover were selected to assess financial leverage and liquidity, key factors in determining a sector’s resilience to market fluctuations.

These indicators were selected based on their established relevance in the financial literature and their alignment with our goal of understanding sectoral stability.

ROA = (Net Income)/(Total Assets)

(1)

Similarly, the ROE, or Return on Equity, measures the capacity of a company to generate profits from net equity. In other words, it assesses the company’s ability to derive benefits from the capital invested by shareholders, thus evaluating the quality of its performance in this regard.

ROE = (Net Profit × 100)/(Net Equity)

(2)

The Sales Ratio is a key financial indicator that assesses a company’s efficiency in utilizing its assets to generate revenue. It is calculated as the ratio of Total Sales to Total Assets:

Sales Ratio = (Total sales)/(Total assets)

(3)

This ratio provides a snapshot of operational efficiency, indicating how effectively a company converts its asset base into sales. A higher ratio suggests more efficient use of assets in generating revenue, while a lower ratio may point to underutilization or inefficiencies in asset management. This metric is vital for comparative analysis, both within a company over time and against industry benchmarks, offering insights into competitive positioning and strategic effectiveness.

However, considering the accounting indicators related to risk measurement, the following ones should be highlighted:

The Working Capital and Cash Conversion Cycle are indicators that quantify solvency from the perspective of a company’s liquidity (Cash Conversion Cycle) and its ability to meet short-term obligations (Working Capital).

Working Capital = Current Asstes − Current Liabilities

(4)

The Working Capital, on the other hand, calculates the disparity between current assets and current liabilities, that is, the number of resources the company possesses to finance its operations within a year. If the Working Capital is high, it indicates that the company has sufficient capacity to meet its financial obligations and, therefore, is considered a less risky investment. Following the same reasoning, a low or negative Working Capital could suggest that the company is facing difficulties in financing its operations, thereby increasing the investment risk.

On the other hand, the Accounts Receivable Turnover offers insights into the efficiency of a company’s credit and collection processes. This ratio is pivotal in evaluating the liquidity and credit risk associated with the company’s receivables.

Accounts Receivable Turnover = (Net credit sales)/(Average Accounts Receivable)

(5)

Additionally, Cash Conversion Cycle measures the time elapsed from when a company makes a payment until it receives payment for its sales, serving as an indicator of the company’s efficiency in managing its accounts receivable and inventories. If the Cash Conversion Cycle is shortened, it indicates that the company is facing difficulties in collecting its accounts receivable or encountering issues with inventory management, which increases the investment risk.

Cash Cycle = Days Payable Outstanding − Days Sales Outstanding

(6)

Days Pable Outstanding = (Accounts Payable)/Purchases × 365 days/year

(7)

Days Sales Outstanding = (Accounts Receivable)/(Operating Revenue) × 365 days/year

(8)

The Supplier Payment Period, a critical liquidity management metric, quantitatively assesses the average duration required by a corporation to settle its accounts payable. The computation of this ratio is as follows:

Supplier Payment Period = (Accounts Payable)/(Cost of Sales) × 365

(9)

This period serves as an indicator of the company’s cash flow management strategies and working capital efficiency. An extended payment period may denote a strategic utilization of trade credit to optimize working capital, whereas a truncated period could indicate a policy of swift supplier remuneration, potentially to secure advantageous credit terms or to fortify supplier relations.

The Cost of Sales Ratio is an essential indicator within financial analyses, denoting the proportion of direct production costs relative to total sales revenue. It is articulated as:

Cost of Sales Ratio = (Cost of Goods Sold)/(Total Sales)

(10)

This ratio elucidates the company’s efficiency in managing direct production costs and the effectiveness of its operational strategies in maximizing gross profitability. A diminished ratio signals a superior margin between production expenses and sales, indicative of heightened gross profitability and effective resource utilization.

The Debt Ratio, a measure of financial leverage, elucidates the proportion of a company’s assets financed through debt. The formulation of this ratio is:

Debt Ratio = (Total Debt)/(Total Assets)

(11)

This ratio is indispensable in evaluating a firm’s financial risk profile and capital structure. An escalated Debt Ratio may suggest a heightened dependence on debt financing, connoting increased financial precariousness and elevated risk exposure for creditors. Conversely, a reduced Debt Ratio implies a more prudent financial posture with reduced reliance on external borrowings, typically associated with enhanced financial solvency and stability.

In aggregate, the Supplier Payment Period, Cost of Sales Ratio, and Debt Ratio are vital in dissecting a company’s financial stewardship, operational efficiency, and leverage strategy. These metrics collectively offer profound insights into the financial robustness, risk management, and strategic fiscal directives of an enterprise.

3.3.3. Descriptive Statistics

Detailed descriptive statistics, including sectoral centrality scores, financial ratios, and performance metrics, are summarized below. Extended tables with complete descriptive statistics are provided in Appendix A, Appendix B and Appendix C to maintain clarity in the presentation of the main methodology. Noteworthy findings include the following:

High-centrality firms such as BHARTI AIRTEL LIMITED (telecommunications) and AMBEV SA (retail) were identified as key influencers, with eigenvector centrality scores of 0.9615 and 0.9938, respectively.

Sectors dominated by high-centrality firms demonstrated a 20% increase in risk-adjusted returns compared to sectors with lower centrality scores, underscoring the stabilizing effect of these firms.

For the Technological Sector, the data reveal varied financial management practices and performance levels. The mean Cash Conversion Cycle (CCC) stands at 27.17 days, yet the broad standard deviation suggests disparate efficiency in cash flow management among these tech entities. The Accounts Receivable average closely aligns with the median, indicating a consistent collection timeframe across firms. A notable mean in the Cost of Sales, paired with a large standard deviation, points to a wide range of cost structures, likely reflective of diverse business models within the technology sector. The Debt Ratio’s average of 22.42% signals a moderate leverage among these companies, with some variance indicative of different capital structures or stages of growth. The Working Capital mean suggests that, on average, firms maintain substantial liquidity to sustain operations. However, the substantial interquartile range indicates liquidity positions vary significantly among these entities. The Supplier Payment Period’s extended mean, compared to a lower median, may imply that some companies strategically extend their payables to optimize cash flow. Return on Assets (ROA) and Return on Equity (ROE) portray averages of 11.79% and 21.34%, respectively, reflecting a spectrum of operational efficiency and profitability. The Sales figures, with a high mean yet right-skewed distribution, underscore the sales volume disparities, possibly due to varying market reaches and product portfolios. In aggregate, these descriptive statistics offer insights into the financial nuances and operational dynamics characteristic of the contemporary technology sector.

The financial indicators for the energy sector exhibit substantial heterogeneity. The mean Cash Conversion Cycle (CCC) is 23.69 days, yet a high standard deviation signifies disparate cash flow efficiencies. Accounts Receivable averages 40.79 days, with a lower median indicating skewedness towards quicker collections. The Cost of Sales has a high mean, suggesting sizeable operational outputs with considerable variation in cost efficiency. Working Capital displays wide fluctuations, including negative values, reflecting diverse financial management strategies. The Debt Ratio mean hovers around 5, denoting moderate but unevenly distributed leverage across firms.

The mean Supplier Payment Period is 78.51 days, indicative of varied credit terms. Returns on Assets (ROA) and Equity (ROE) present means of 5.48% and 11.72%, respectively, with ROE’s broader variance suggesting differential profitability and asset performance. Sales data, with a high mean, point to significant revenue generation but with pronounced disparities, underscoring the presence of dominant market participants. The interquartile ranges further corroborate the financial diversity within the energy sector’s corporate landscape.

In an empirical assessment of the industrial sector’s financial health, the dataset delineates a pronounced mean Cash Conversion Cycle (CCC) of 492 days. The expansive standard deviation accompanying this mean suggests a vast disparity in the sector’s operational liquidity cycles. The median for Accounts Receivable, substantially lower than the mean, reflects a skewness towards a majority of firms with more conservative credit collection practices, despite some outliers extending longer terms.

The Cost of Sales metric reveals a high mean, indicative of the sector’s sizable production volume, while the substantial standard deviation underscores the cost structure diversity across the sampled companies. The Working Capital metric, while averaging positively, exhibits a range that includes negative values, pointing to operational financing challenges for certain entities within the sector. The Debt Ratio presents an average slightly above 24%, signifying a moderate but uneven use of leverage among the firms.

The Returns on Assets (ROA) and Equity (ROE) display averages of 5.44% and 10.71%, respectively. These figures, together with their associated standard deviations, suggest a spectrum of operational efficiency and profitability. The Sales variable, with its high mean, confirms robust sector-wide revenue generation capacity; yet, the wide-ranging data imply significant revenue disparities, reflective of the sector’s diverse market presence and operational scale. The interquartile range in several of these metrics further attests to the financial performance variability within the industrial sector.

For the mining sector, descriptive statistics exhibit a wide range in financial performance. The Cash Conversion Cycle averages 114.82 days with substantial variation, suggesting differences in liquidity management. Accounts Receivable and Cost of Sales figures reflect divergent credit and cost strategies, while the positive mean Working Capital indicates sufficient liquidity amidst a range of operational efficiencies. The Debt Ratio, at an average of 27%, along with ROA and ROE means of 8.91% and 13.81%, respectively, point to varied profitability and leverage across the sector. Finally, the Sales data, while high on average, indicate significant revenue disparities, underscoring the diverse scales of operation within the mining industry.

In the retail sector, the data suggest a skewed Cash Conversion Cycle with a high mean of 278 days influenced by outliers, as evidenced by a much lower median. Accounts Receivable averages around 23 days, indicating relatively consistent collection practices. The mean Cost of Sales is significant, mirroring the high operational throughput characteristic of the sector, yet the variance denotes diverse cost management. Working Capital and Debt Ratio averages suggest financial prudence, though with some firms exhibiting liquidity constraints. Supplier Payment Periods and profitability metrics like ROA and ROE display considerable averages but with substantial variability, reflecting the heterogeneous nature of retail operations and financial performance. Sales data, while high on average, reveal the diverse scale of entities within the sector.

Finally, for the telecommunications sector, the financial data illustrate a complex picture: A Cash Conversion Cycle with a small mean but high variance indicates inconsistent cash flow management. Accounts Receivable suggests a typical billing cycle with moderate variability among companies. The Cost of Sales indicates substantial but consistent operational expenses. Working Capital is on average negative, hinting at potential liquidity challenges within the sector. A Debt Ratio averaging 28% reflects varied leverage, while profitability measures such as ROA and ROE show wide-ranging performance across companies. Finally, Sales volumes are substantial but diverse, mirroring the varying scales of operations within the industry.

3.4. Empirical Methodology

Within the ambit of econometric inquiry, the present analysis meticulously integrates a network-theoretic paradigm to dissect the intricacies of corporate financial interconnectivity. Central to this endeavor are three network centrality metrics, each offering a distinct vantage point from which to survey the labyrinthine corporate networks.

The investigation’s analytical arsenal is fortified by the incorporation of the eigenvector centrality, a metric that extends beyond the superficial ties of fiscal interactions, delving into the essence of corporate influence. Here, the concept of centrality transcends mere connections, delving into the qualitative realm where the company’s influence is augmented by the stature of its associates in the network hierarchy.

Interposing this advanced methodological consideration, we bridge the foundational measures of network centrality with their profound implications for corporate influence and market dynamics. The meticulous calibration of these centrality metrics provides a robust scaffold upon which the structural nuances of corporate interconnectedness are unveiled, laying bare the nodes of influence that sculpt the financial landscape.

With this pivotal conceptual segue, we transition from the theoretical underpinnings of network centrality to its pragmatic application in the economic sphere. It is within this nexus that eigenvector centrality emerges as a beacon, guiding the analysis through the dense thicket of corporate networks to identify not just the prominent players but also the subtler forces at play that dictate market currents and undercurrents.

Eigenvector centrality is articulated as a recursive index of influence, where the centrality of a node v is contingent upon the sum of the centralities of its directly connected nodes. It is formally defined by the following equation:

$$EC\left(v\right)={\displaystyle \frac{1}{⋋}}{\sum }_{t\in M\left(v\right)}EC\left(t\right)$$

(12)

where M(v) enumerates the neighbors of v and ⋋ stands as a scaling eigenvalue. This metric distinguishes itself by recognizing not merely the quantity but the quality of a node’s connections, ascertaining a form’s potential to be an epicenter of influence by virtue of its network position.

Betweenness Centrality (BC), notated as BC(v), quantifies the frequency with which a node v presides over the shortest communicative paths between other node pairs. This is encapsulated in the following formula:

$$BC\left(v\right)={\sum }_{s,t\in V}{\displaystyle \frac{{\sigma }_{st}\left(v\right)}{{\sigma }_{st}}}$$

(13)

Hence, V is the set of nodes, σ_st(v) tallies the total shortest paths from nodes s to node t, and σ_st(v) counts the number of those paths traversing trough node v. BC illuminates nodes that serve as pivotal brokers of information, potentiality wielding considerable sway over the dissemination of financial intelligence.

Closeness Centrality (CC), represented by CC(v) gauges the degree to which a node is in proximity, in terms of path length, to all other nodes with the network. It is given by the following expression:

$$CC\left(v\right)={\displaystyle \frac{N-1}{{\sum }_{t\in V\setminus \left\{v\right\}}d(v,t)}}$$

(14)

with N symbolizing the total nodes, and d(v,t) denoting the shortest-path distance between modes v and t. CC sheds light on nodes that can rapidly assimilate and propagate shifts in the market, due to their central position in the network’s topology.

We applied eigenvector centrality to assess sectoral influence within the financial network, using the following approach:

Network Construction: A correlation matrix was built based on the Pearson correlation of sectoral returns to model the relationships between firms.

Eigenvector Centrality Calculation: We used the power iteration algorithm in Python 3.12.3 (via the NetworkX library) to compute eigenvector centrality, identifying the most influential sectors within the network.

Additionally, Euclidean distance was calculated to explore the similarity between firms and refine the analysis of sectoral interconnections.

3.4.1. Methodological Framework for Applying Eigenvector Centrality Derived from Correlation Matrices in Financial Network Analysis

The computation of eigenvector centrality (EC) in the context of corporate financial networks commences with the construction of a correlation matrix C. This matrix is derived from the correlation coefficients between the financial returns of various firms, with each element c_ij in C denoting the correlation between firms i and j. This mathematical construct encapsulates the financial interdependencies among firms, thereby enabling a detailed examination of the underlying relational structure.

• Construction of Correlation Matrix

The Correlation Matrix C is formulated as follows

$$C=\left[\begin{array}{ccc}{c}_{11}& \cdots & c_{1n}\\ ⋮& \ddots & ⋮\\ c_{n1}& \cdots & c_{nn}\end{array}\right]$$

(15)

where each element $c_{ij}$ resents the Pearson correlation coefficient between the financial returns of firms $i$ and $j$:

$$C_{ij}={\displaystyle \frac{COV(R_i,R_j)}{{\sigma }_i{\sigma }_j}}$$

(16)

In this equation, $COV(R_i,R_j)$ denotes the covariance of returns between firms $i$ and $j$, and ${\sigma }_i$ and ${\sigma }_j$ are the standard deviations of the returns of firms $i$ and $j$, respectively.

• Eigenvalue Decomposition

To derive the eigenvector centrality from the matrix C, an approach based on the calculation of eigenvalues and eigenvectors is employed. This involves the eigenvalue decomposition of C:

$$C_{vk}={\lambda }_k{v}_k$$

(17)

where $v_k$ represents the $k$-th eigenvector and ${\lambda }_k$ is the corresponding eigenvalue.

• Principal eigenvector

The eigenvector corresponding to the largest eigenvalue ${\lambda }_{max}$ is selected as the principal eigenvector $v_{max}$:

$$C_{Vmax}={\lambda }_{max}{v}_{max}$$

(18)

• Eigenvector Centrality Scores

Each component $v_i$ of the principal eigenvector $v_{max}$ represents the eigenvector centrality score for node $i$:

$$EC\left(v_i\right)=v_{max,i}$$

(19)

This principal eigenvector, termed the eigenvector centrality vector, assigns to each node a score proportional to its influence within the network. The underlying premise is that a node’s influence is amplified if it is connected to highly central nodes, thereby emphasizing the importance of the quality of connections over their mere quantity.

This methodological approach not only elucidates the relative positions of influence of each entity within the financial network but also facilitates a deeper interpretation of how the structure of interrelations influences the overall system dynamics. Consequently, the analysis using the correlation matrix and eigenvector centrality emerges as a powerful tool for deciphering the complex networks of financial interactions. This method accentuates entities that, although may not be prominent in terms of direct connectivity, exert significant influence through their high-quality connections.

3.4.2. Methodology for Determining Eigenvector Centrality Using Euclidean Distances

The integration of eigenvector centrality (EC) with Euclidean distance methodologies within the context of financial neural networks represents a sophisticated approach to elucidating complex interdependencies and influence patterns in financial markets. This methodology leverages the strengths of EC to assess influence based on the quality of connections within the network while utilizing Euclidean distances to quantify the similarity between financial entities, thus providing a multidimensional perspective on market dynamics. The application of this integrated approach in neural network models facilitates a nuanced analysis of financial systems, where nodes represent financial entities and edges denote the relationships or flows between them, informed by both transactional interactions and attribute-based similarities.

• Construction of the Euclidean Distance Matrix

The analytical process begins with the construction of a neural network model that encapsulates financial entities as nodes. The network’s structure is informed by transactional data and attribute similarities. The Euclidean distance matrix $D$ is derived from multidimensional financial attributes, such as risk profiles or asset compositions. Each element $d_{ij}$ in $D$ represents the Euclidean distance between entities $i$ and $j$:

$$d_{ij}=\sqrt{{\sum }_{k=1}^m{(x_{ik}-x_{jk})}^2}$$

(20)

where $x_{ij}$ and $x_{jk}$ are the values of the $k$-th attribute for entities $i$ and $j$, respectively, and $m$ is the number of attributes.

• Transformation to a Similarity Matrix

The Euclidean distance matrix $D$ is then transformed into a similarity matrix $S$. This transformation involves inverting the distance values to reflect similarity:

$$S_{ij}={\displaystyle \frac{1}{1+d_{ij}}}$$

(21)

where $s_{ij}$ denotes the similarity between entities $i$ and $j$.

• Construction of the Weighted Adjacency Matrix

The similarity matrix $S$ is used to adjust the weights of connections between nodes in the neural network model, resulting in a weighted adjacency matrix $A$. This matrix encapsulates both transactional strength and attribute similarity:

$$A=S\circ T$$

(22)

where $\circ$ denotes the element-wise multiplication and $T$ represents the transactional interaction matrix.

• Spectral Decomposition of the Weighted Adjacency Matrix

The core of this methodology involves the spectral decomposition of the weighted adjacency matrix $A$:

$$A_{vk}={\lambda }_k{v}_k$$

(23)

where $v_k$ is the $k$-th eigenvector and ${\lambda }_k$ is the corresponding eigenvalue.

• Identification of the Principal Eigenvector

The eigenvector corresponding to the largest eigenvalue ${\lambda }_{max}$ is designated as the principal eigenvector $v_{max}$:

$${Av}_{max}={\lambda }_{max}{v}_{max}$$

(24)

• Calculation of Eigenvector Centralities

Each component $v_i$ of the principal eigenvector $v_{max}$ is interpreted as the eigenvector centrality score for node $i$:

$$EC\left(v_i\right)=v_{max,i}$$

(25)

This eigenvector, termed the eigenvector centrality vector, assigns to each node a score proportional to its influence within the network. The underlying premise is that a node’s influence is magnified if it is connected to highly central nodes, thereby emphasizing the importance of the quality over the quantity of connections.

This methodological approach not only elucidates the relative positions of influence of each entity within the financial network but also facilitates a deeper interpretation of how the structure of interrelations influences the overall system dynamics. Consequently, the analysis using the Euclidean distance matrix and eigenvector centrality becomes a powerful tool for deciphering the complex networks of financial interactions. This method accentuates entities that, although they may not be prominent in terms of direct connectivity, exert significant influence through their high-quality connections.

To ensure the robustness of our findings, we implemented multiple validation techniques:

Bootstrap Resampling: Centrality scores were recalculated across 1000 random subsamples of the data to test the stability of the results.

Variance Inflation Factor (VIF): This was used to check for multicollinearity between financial indicators, ensuring that no variable redundancy skewed the centrality measurements.

3.4.3. Limitations and Potential Biases

Several limitations should be acknowledged:

Sampling Bias: The dataset is restricted to publicly listed firms, which introduces a potential bias by disproportionately representing larger, well-established companies. This could lead to an underestimation of the role played by smaller firms and private entities, which may also exert significant influence within their respective sectors but are not captured by the current data.

Temporal Scope: The analysis spans the period from 2013 to 2022, providing a snapshot of financial and sectoral dynamics over this timeframe. However, this limited scope may fail to capture longer-term structural shifts, cyclical market patterns, or the evolving nature of sectoral interdependencies that extend beyond this decade. Future studies incorporating a longer historical period could offer deeper insights into how these networks evolve over time.

Model Limitations: While graph theory provides a powerful quantitative framework for analyzing sectoral interconnections, it inherently simplifies the complexities of financial systems. By focusing primarily on numerical relationships, the model does not account for qualitative factors such as corporate governance practices, regulatory environments, or geopolitical influences, which may significantly affect sectoral performance and market stability. Incorporating these dimensions in future analyses could provide a more holistic understanding of financial networks.

4. Results

The analysis of eigenvector centrality across sectors provided profound insights into the financial networks of emerging markets, revealing the pivotal role that select firms play within their respective sectors. To streamline the discussion, we focus on key results, emphasizing firms with significant centrality. Specifically, BHARTI AIRTEL LIMITED in telecommunications and AMBEV SA in retail stood out with eigenvector centrality scores of 0.9615 and 0.9938, respectively, underscoring their dominant positions within the network. These firms not only exhibited greater sectoral stability but also contributed to a 20% increase in risk-adjusted returns, thereby reinforcing the critical connection between centrality and financial performance. See the following

Table 2. Graph results. Correlation methodology. First company.

			First Company
Sectors	Binomial	Countries	Central Company	Central Country	Value
Technological	Profitability	India, South Africa, Russia	Brwegeacnor	Brazil	0.980127726
	Risk		Naspers Ltd-N Shs.	South Africa	0.75209742
Energy	Profitability	Brazil, China, India, UAE i Saudi Arabia, Russia	Petrochina Co., Ltd.-A.	China	0.99328132
	Risk		Sasol Ltd.	South Africa	0.987490199
Industrial	Profitability	India, Egypt, Russia	Saudi Basic Industries Corp	Saudi Arabia	0.997048971
	Risk		China Yangtze Power Co., Ltd.	China	0.988176758
Mining	Profitability	Saudi Arabia, Egypt, Rusia	Gold Fields Ltd.	South Africa	0.998320544
	Risk		Gold Fields Ltd.	South Africa	0.90673491
Retail	Profitability	Brazil, UAE, India, South Africa, Russia	Kweichow Moutai Co., Ltd.	China	0.964393777
	Risk		Bid Corp Ltd.	South-Africa	0.283998512
Telecommunications	Profitability	UAE, India, Saudi Arabia, Egypt	Telecom Egypt	Egypt	0.961497952
	Risk		Telecom Egypt	Egypt	0.86280219

Source: Prepared by the authors.

for detailed results.

This table presents the central companies identified through the correlation methodology, which highlights the most influential firms based on their centrality metrics. The analysis is divided into sectors, examining both profitability and risk.

To enhance the interpretative strength of the results, we incorporated additional statistical measures to validate the robustness of the centrality scores. A bootstrap resampling technique was employed to estimate confidence intervals, ensuring the reliability of the findings. For instance, the centrality score of BHARTI AIRTEL LIMITED was confirmed with a 95% confidence interval of [0.952, 0.970], affirming the firm’s critical influence within the financial network. Moreover, the correlation between eigenvector centrality and sectoral stability—as measured by volatility—was statistically significant, with a p-value below 0.01, indicating a strong and reliable relationship between network centrality and market resilience.

These statistical validations add significant weight to the hypothesis that highly central firms serve as stabilizing agents within their respective sectors, reinforcing both sectoral robustness and profitability. See the following

Table 3. Graph results. Correlation methodology. Second company.

			Second Company
Sectors	Binomial	Countries	Central Company	Central Country	Value
Technological	Profitability	India, South Africa, Russia	Anglogold Ashanti Plc	South Africa	0.153907402
	Risk		Weg Sa	Brazil	0.330958721
Energy	Profitability	Brazil, China, India, UAE and Saudi Arabia	China Petroleum & Chemical-A.	China	0.088530711
	Risk		Reliance Industries Ltd.	India	0.935532422
Industrial	Profitability	India, Egypt, Russia	China Yangtze Power Co., Ltd.-A	China	0.068809553
	Risk		T M G Holding	Egypt	0.157511471
Mining	Profitability	Saudi Arabia, Egypt, Russia	Vale Sa.	Brazil	0.047139508
	Risk		Vale Sa.	Brazil	0.241040974
Retail	Profitability	Brazil, UAE, India, South Africa and Russia	Ambev Sa	Brazil	0.020614607
	Risk		Hindustan Unilever Limited	India	0.058156299
Telecommunications	Profitability	UAE, India, Saudi Arabia, Egypt, Russia	Saudi Telecom Co	Saudi Arabia	0.288342831
	Risk		Bharti Airtel Limited	India	0.580035465

Source: Prepared by the authors.

for the correlation results and

Table 4. Graph results. Euclidean distance methodology. First company.

			First Company
Sectors	Binomial	Countries	Central Company	Central Country	Value
Technological	Profitability	India, South Africa, Russia	Larsen & Toubro Limited	India	0.990489071
	Risk		Infosys Technologies Ltd.	India	0.94525552
Energy	Profitability	Brazil, China, India, UAE Saudi Arabia	Elswedy Electric Co	Egypt	0.937319886
	Risk		Elswedy Electric Co	Egypt	0.977412161
Industrial	Profitability	India, Egypt and Russia	Misr Fertilizers Production	Egypt	0.999741014
	Risk		Misr Fertilizers Production	Egypt	0.9878176765
Mining	Profitability	Saudi Arabia, Egypt and Russia	Anglogold Ashanti Plc	South Africa	0.91953331
	Risk		Abou Kir Fertil & Chemicals	Egypt	0.983342945
Retail	Profitability	Brazil, UAE, India, South Africa	Ambev Sa	Brazil	0.993818947
	Risk		Bid Corp Ltd.	South Africa	0.988690132
Telecommunications	Profitability	UAE, India, Saudi Arabia, Egypt and Russia	Bharti Airtel Limited	India	0.986665956
	Risk		Mtn Group Ltd.	South Africa	0.935138578

Source: Prepared by the authors.

and

Table 5. Graph results. Euclidean distance methodology. Second company.

			Second Company
Sectors	Binomial	Countries	Central Company	Central Country	Value
Technological	Profitability	India, South Africa	Weg Sa	Brazil	0.987422877
	Risk		Naspers Ltd-N Shs	South Africa	0.865935312
Energy	Profitability	Brazil, China, India, UAE, Saudi Arabia and Russia	Centrais Eletricas Brasilier	Brazil	0.778368913
	Risk		Centrais Eletricas Brasilier	Brazil	0.722266532
Industrial	Profitability	India, Egypt and Russia	China Yangtze Power Co., Ltd.	China	0.147042953
	Risk		T M G Holding	Egypt	0.855257344
Mining	Profitability	Saudi Arabia, Egypt and Russia	Abou Kir Fertil & Chemical	Egypt	0.831333518
	Risk		Abou Kir Fertil & Chemicals	Egypt	0.983342945
Retail	Profitability	Brazil, UAE, India, South Africa and Russia	Bid Corp Ltd.	South Africa	0.988690132
	Risk		Ambev Sa	Brazil	0.974036596
Telecommunications	Profitability	UAE, India, Saudi Arabia and Egypt	Saudi Telecom Co	Saudi Arabia	0.869532696
	Risk		Gulf Navigation Holding	UAE	0.89041937

Source: Prepared by the authors.

for the Euclidean distance methodology.

This table highlights the central companies identified through Euclidean distance.

While this study spans multiple sectors, the specific methodological approach applied to each sector is critical to understanding the financial networks in these emerging markets. By employing eigenvector centrality and Euclidean distance, we quantify the degree of interconnectedness and similarity between firms.

For instance, in the telecommunications sector, BHARTI AIRTEL LIMITED emerged as a central node with an eigenvector centrality score of 0.9615, significantly influencing the sector’s overall stability. In contrast, firms in the energy sector showed lower centrality scores (e.g., Petrobras with a centrality score of 0.6132), reflecting weaker sectoral integration and higher susceptibility to external shocks. These quantitative results highlight the disparity in sectoral stability and emphasize the pivotal role of highly central firms.

• Comparative Analysis and Sectoral Insights

To provide a more granular understanding of the results, we conducted a comparative analysis between sectors and contrasted these findings with existing studies. For example, Wang et al. (2024) found that centrality metrics in developed markets are more evenly distributed, while our results suggest a higher concentration of influence in emerging markets. This supports the notion that financial networks in emerging economies are more fragile, with fewer firms shouldering a disproportionate amount of market stability.

In addition, sectors like telecommunications and retail showed stronger network cohesion, while energy and basic materials exhibited fragmentation. This suggests that sectoral centrality is closely tied to the underlying market dynamics and regulatory environments, a key insight for both investors and policymakers aiming to enhance market resilience.

• Integration with Existing Literature and Theoretical Context

The findings of this study are deeply embedded within the broader theoretical frameworks of network theory and market integration. Our use of eigenvector centrality extends this argument to the financial networks of emerging economies, showing that firms with higher centrality not only stabilize their sectors but also enhance profitability.

Moreover, the application of Euclidean distance offers a complementary lens through which to examine financial similarity. By measuring the proximity of firms within a multidimensional financial space, we validate the hypothesis that firms with similar financial health are often more closely connected within the network, as seen in the telecommunications sector. This dual-method approach aligns with recent advances in network analysis and provides a comprehensive framework for understanding sectoral dynamics.

• Justification for Methodological Choices

The choice of eigenvector centrality and Euclidean distance is not arbitrary but is instead grounded in both the theoretical literature and the specific objectives of this study. Eigenvector centrality allows us to capture not only the direct connections between firms but also the importance of a firm’s neighbors within the financial network, making it particularly suited for analyzing sectoral influence. In contrast, Euclidean distance offers a quantitative measure of how similar or dissimilar firms are in terms of financial performance, providing a multidimensional view of sectoral cohesion.

The integration of these methods enables us to capture the complex interplay between influence and similarity within financial networks. For example, firms with high centrality scores tended to exhibit shorter Euclidean distances, indicating that influential firms also share similar financial characteristics, further reinforcing the network’s stability.

• Sector-Specific Applications

Each sector analyzed in this study presents unique implications for both investors and policymakers:

In telecommunications, where firms like BHARTI AIRTEL LIMITED exhibit high centrality, the findings suggest opportunities for risk-adjusted investment strategies targeting central firms that drive market stability.

In contrast, sectors like energy require a more cautious approach due to their fragmented network structure and higher volatility, as evidenced by the lower centrality scores of firms like Petrobras. This suggests the need for targeted regulatory interventions to enhance sectoral integration and reduce systemic risks.

By integrating insights across sectors, this study provides a comprehensive framework for understanding the multifaceted nature of market integration in emerging economies. The ability to pinpoint highly central firms offers actionable insights for portfolio optimization and the design of policies aimed at strengthening market resilience.

• Comparative Recommendations and Future Research Directions

Comparing our findings with previous studies highlights the need for further investigation into the structural differences between emerging and developed markets. While central firms in emerging markets exert significant influence, future research should explore how institutional factors—such as regulatory frameworks and corporate governance—shape these networks. Additionally, cross-market comparisons could yield insights into how emerging markets evolve as their financial systems mature.

This study has laid the groundwork for further exploration into the role of central firms within global financial networks, offering a template for more sector-specific research that could better inform both investment strategies and economic policies.

• Interpretation of Results in the Context of Market Integration

This section provides a thorough examination of the empirical findings from our study, focusing on their implications for the financial markets of the BRICS nations and emerging economies such as Egypt, Saudi Arabia, and the UAE. The results are analyzed in terms of their broader applications, emphasizing their relevance for policy and investment strategy formulation.

The findings presented here offer substantial implications for the broader discussion on market integration in emerging economies. The concentration of influence among a small subset of highly central firms, such as BHARTI AIRTEL LIMITED and AMBEV SA, suggests that these firms act as anchor points within their sectors, facilitating market stability and enhancing the overall connectivity of financial networks. The observed relationship between centrality and enhanced profitability points to a non-linear dynamic within emerging markets, where the influence of a few firms can disproportionately shape sectoral outcomes.

This structural concentration also underscores the systemic vulnerability of these markets. A disruption affecting any of these highly central firms could trigger widespread volatility, given their outsized impact on market stability. Consequently, both investors and policymakers must consider the network centrality of firms when formulating strategies for risk mitigation and growth optimization. By targeting these central firms, stakeholders may be able to enhance financial resilience and minimize systemic risks across the broader market.

• Cross-Sectoral Comparisons and Insights

A comparative analysis of sectors revealed notable variations in the degree of integration into the broader financial network. Sectors such as telecommunications and retail demonstrated the highest levels of centrality, indicating stronger sectoral cohesion and stability, while sectors such as energy and basic materials exhibited lower centrality scores, pointing to weaker integration and higher volatility.

For example, firms in the telecommunications sector, such as BHARTI AIRTEL LIMITED, displayed high centrality values correlated with reduced market volatility, thereby contributing to a more stable sectoral environment. Conversely, the energy sector showed a more fragmented network structure, with lower centrality scores and higher susceptibility to market shocks. These differences highlight the heterogeneous nature of market integration across sectors in emerging economies, where certain industries act as linchpins for stability, while others remain more vulnerable to external disruptions.

• Methodological Integration of Correlation and Euclidean Distance

To obtain a comprehensive understanding of the financial networks, we employed both correlation analysis and Euclidean distance. The correlation matrix was used to capture the co-movements in sectoral returns, whereas Euclidean distance provided a quantitative measure of the similarity in financial profiles between firms. These complementary methodologies allowed us to discern not only how closely firms’ returns moved together but also how similar they were in terms of underlying financial health.

Sectors with firms exhibiting high centrality were found to have shorter Euclidean distances, indicating a tighter clustering of firms with similar financial structures. This dual analysis, leveraging both correlation and distance metrics, enriches the overall understanding of how centrality and similarity interact within financial networks, reinforcing the notion that highly connected firms often share similar financial attributes, thus contributing to sectoral stability.

4.1. Sectorial Insights

Our research yields critical insights into the centrality and influence of key corporations across various sectors by utilizing eigenvector centrality correlation and Euclidean distance methodologies. These findings highlight the essential roles these entities play in shaping sectoral profitability and risk dynamics.

• Telecommunications Sector

The telecommunications sector analysis reveals that BHARTI AIRTEL LIMITED and TELECOM EGYPT exhibit high centrality metrics, underscoring their pivotal influence on the sector’s financial health. The Euclidean distance methodology further identifies MTN GROUP LTD as a central entity, indicating its strategic importance within the network. The centrality of these firms underscores their integral role in sector stability and growth, with significant implications for both domestic and international markets.

• Retail Sector

In the retail sector, the analysis highlights the critical positions of AMBEV SA, KWEICHOW MOUTAI Co., Ltd.-A, and BID corp. Ltd. The prominence of these companies in the centrality measures indicates their substantial impact on sectoral stability and profitability. Their central roles imply that their operational performance serves as reliable indicators of broader sectoral trends and market movements, providing valuable insights for stakeholders.

• Energy and Industrial Sectors

In the energy sector, SASOL LTD and SAUDI BASIC INDUSTRIES CORP are identified as key influencers. Similarly, in the industrial sector, SAUDI BASIC INDUSTRIES CORP and CHINA YANGTZE POWER Co., Ltd. emerge as central entities. The significant centrality of these companies reflects their capacity to drive sectoral dynamics, influencing global supply chains and market stability. Understanding their strategic operations and financial performance is crucial for assessing sectoral resilience and risk exposure.

• Mining and Technology Sectors

The mining and technology sectors exhibit a pattern of dispersed centrality. Companies such as GOLD FIELDS LTD, VALE SA, and ANGLOGOLD ASHANTI PLC are prominent in the correlation analysis, while LARSEN & TOUBRO LIMITED stands out in the Euclidean metric. This dispersion indicates a complex network of influence, where multiple entities contribute to sectoral dynamics, enhancing robustness against market volatility.

4.2. Implications for Financial Markets, Investors and Policymakers

The findings underscore the significant role of network centrality in understanding sectoral economic stability. Identified central firms in each sector act as bellwethers, offering critical insights into market trends and potential risks. Investors and policymakers can leverage these insights for strategic decision making, enhancing portfolio management and policy formulation.

The observed inverse relationship between centrality concentration and sectoral innovation capacity, particularly in the mining and technology sectors, suggests that a more equitable distribution of influence fosters a competitive environment conducive to innovation. This underscores the importance of nurturing diverse and interconnected corporate networks to stimulate sectoral growth and innovation.

The systemic impact of sectoral centrality on global market dynamics is evident from the alignment of sectors such as energy and industry with global market trends. The influence of central firms extends beyond their immediate sectors, affecting global economic performance. This emphasizes the need for comprehensive network analysis in global economic modeling and predictive analyses.

Integrating these empirical findings into policy and investment strategies is paramount. Policymakers should consider centrality metrics when formulating economic policies to enhance sectoral stability and growth. Investors can use these insights to inform portfolio diversification and risk management, identifying key firms that drive sectoral and market trends.

The findings presented in this study have critical implications for investment strategies and policy formulation. For investors, the identification of high-centrality firms provides a strategic advantage, offering opportunities to optimize portfolios by targeting firms that exhibit both stability and strong financial performance. These firms, by virtue of their centrality, act as stabilizers within their sectors, offering risk-adjusted returns that outperform their less connected peers.

From a policymaking perspective, understanding the role of central firms in maintaining sectoral stability is crucial for the design of targeted interventions aimed at mitigating systemic risks. Policymakers can leverage these insights to strengthen the resilience of financial networks by ensuring that key firms are adequately supported, thus safeguarding the broader economic ecosystem from potential shocks.

By uncovering the structural underpinnings of financial networks in emerging markets, this study provides a framework for both investors and policymakers to navigate the complexities of market integration, enabling more informed decision making that promotes long-term stability and sustainable growth.

4.3. Comparative Analysis with Relevant Literature

Our findings resonate with and extend the work of several scholars in the field. For instance, Wang et al. (2024) and Bertsche et al. (2022) highlighted the importance of eigenvector centrality in understanding the structural dynamics within emerging markets. Their research demonstrates that high eigenvector centrality within corporate networks is a strong indicator of influence and stability, which our study corroborates by demonstrating the significant influence of key corporations on sectoral stability and profitability. Specifically, we have shown that firms such as BHARTI AIRTEL LIMITED and AMBEV SA play pivotal roles in their respective sectors, mirroring the conclusions drawn by these scholars.

Furthermore, the work of Mamman et al. (2023) and Atale (2012) underscores the challenges and opportunities associated with economic integration among BRICS and emerging market countries. Their analyses highlight how integration can foster economic stability and growth but also expose these economies to global financial volatility. Our study extends this discourse by specifically identifying central firms within these markets and elucidating their strategic significance through detailed empirical data. This aligns with the strategic macroeconomic policymaking needs suggested by Stojković and Milosavljević (2023), emphasizing the importance of leveraging the benefits of integration while mitigating inherent risks.

• Sector-Specific Comparisons

In the telecommunications sector, our findings parallel the insights of Bertsche et al. (2022), who discuss the criticality of network structures in facilitating information flow and operational efficiency. The identification of BHARTI AIRTEL LIMITED and TELECOM EGYPT as central nodes is consistent with their assertion that high-centrality entities are often leaders in innovation and market influence.

In the retail sector, Khan et al. (2022) highlighted the role of multinational corporations in shaping market dynamics. Our identification of AMBEV SA and KWEICHOW MOUTAI Co., Ltd.-A as central firms aligns with their findings that such companies often drive sectoral trends and profitability through extensive supply chains and market reach.

• Theoretical and Methodological Comparisons

Our methodological approach, utilizing both eigenvector centrality correlation and Euclidean distance metrics, complements the theoretical framework provided by Dai (2023). Dai’s work on business cycle synchronization and multilateral trade integration in the BRICS underscores the importance of understanding the intricate web of economic relationships. Our use of advanced graph theory techniques builds upon this foundation, providing a more nuanced understanding of corporate influence and sectoral stability.

Furthermore, the application of graph theory in our study extends the quantitative analysis techniques discussed by Hong (2023), who employs advanced graph theory models to map the global influence of emerging economies. Our findings support Hong’s conclusions by demonstrating how central firms within these networks not only influence their immediate sectors but also have broader implications for global market trends.

• Implications for Policy and Practice

Our research further aligns with studies by Osei and Kim (2023) and Rath et al. (2023), who explore the effects of financial development and ICT convergence on economic growth. Osei and Kim discuss the differentiated impacts of foreign direct investment across varying financial development levels, suggesting that robust financial networks can amplify the benefits of such investments. Our findings on central firms’ roles in sectoral stability and growth resonate with their conclusions.

4.4. Implications for Investors and Policymakers

The findings of this study hold significant implications for both investors and policymakers, providing actionable insights that can enhance decision-making processes and strategic planning in the context of emerging markets.

• Implications for Investors

Portfolio Diversification: By identifying key nodes—pivotal countries or corporations—that significantly influence the economic trajectory within the BRICS and emerging economies, investors can make informed decisions about portfolio diversification. Understanding which entities have a central role in the economic network helps investors to allocate their resources more efficiently, potentially reducing risk and enhancing returns.

Risk Management: This study highlights the interconnectedness of various economies and sectors. Investors can use this information to better understand systemic risks and vulnerabilities within their portfolios. Recognizing how central entities influence market dynamics enables investors to implement more effective risk management strategies, such as hedging against potential market volatilities.

Strategic Investment: Insights into sectoral centrality and influence can guide investors in identifying growth opportunities. Sectors or companies identified as having high eigenvector centrality might be seen as more stable or influential, making them attractive targets for long-term investment. Conversely, understanding the risks associated with certain centralities can help avoid overexposure to volatile segments.

• Implications for Policymakers

Policy Formulation: Policymakers can use the findings to develop targeted economic policies that support stability and growth. By understanding the pivotal role of certain countries or sectors, they can design policies that strengthen these key areas, thereby enhancing overall economic resilience. Policies that encourage innovation and competitiveness in central sectors can lead to broader economic benefits.

Economic Integration: This study underscores the importance of strategic macroeconomic policymaking in facilitating economic integration. Policymakers can leverage these insights to foster international cooperation and align national policies with global economic trends. This approach can help mitigate the risks associated with financial volatility and policy spillovers, ensuring smoother integration into the global financial system.

Regulatory Measures: The identification of influential nodes within the economic network can inform regulatory frameworks. Policymakers can develop regulations that ensure the stability of these central entities, thus safeguarding the broader economic network. Ensuring robust corporate governance and financial transparency in key companies can prevent systemic risks and promote investor confidence.

• Strategic Importance

The strategic insights derived from this study are invaluable for both investors and policymakers. For investors, these insights facilitate better resource allocation, risk management, and identification of growth opportunities. For policymakers, the findings provide a basis for formulating effective economic policies, fostering international cooperation, and implementing robust regulatory measures. By understanding the centrality and influence within the economic network, stakeholders can navigate the complexities of an interconnected global economy more effectively, promoting sustainable growth and stability.

5. Conclusions

This study provides an in-depth analysis of the financial networks in emerging markets by applying graph theory, specifically eigenvector centrality and Euclidean distance, to evaluate the interconnectedness and influence of firms across sectors. The findings reveal that high-centrality firms, such as BHARTI AIRTEL LIMITED in telecommunications and AMBEV SA in retail, play a critical role in stabilizing their sectors and enhancing profitability. The centrality scores for these firms (e.g., 0.9615 and 0.9938, respectively) not only confirm their dominant positions but also correlate with a 20% increase in risk-adjusted returns, highlighting their impact on sectoral performance.

A key insight from the analysis is the disparity in sectoral integration. Sectors like telecommunications and retail demonstrate strong network cohesion and stability, while sectors such as energy and basic materials show lower centrality scores, higher volatility, and fragmentation. These variations underscore the uneven distribution of influence within emerging market economies, where a few central firms disproportionately contribute to market resilience.

This study extends the literature on financial integration and network theory by providing empirical evidence on the role of centrality in emerging markets. Previous studies, such as those by Wang et al. (2024), focused on developed markets, where financial networks tend to be more evenly distributed. In contrast, our findings suggest that emerging markets exhibit a higher concentration of central firms, which are pivotal in maintaining sectoral stability and market integration.

The application of eigenvector centrality builds upon theoretical foundations that emphasize the role of central nodes in stabilizing networks. However, this study extends beyond these frameworks by demonstrating that, in emerging markets, the role of central firms is even more pronounced due to fragile institutional structures and less mature financial systems. This heightened reliance on a small number of firms for market stability presents both opportunities and risks, suggesting that policymakers and investors must carefully consider these central nodes when making strategic decisions.

Additionally, this research integrates Euclidean distance as a complementary measure, offering a novel way to assess financial similarity within sectors. By combining centrality with financial similarity, this study provides a multidimensional perspective on sectoral dynamics, which enhances our understanding of how firms within the same sector interact and influence each other. This approach contributes to the growing field of multilayer network analysis, suggesting that future research could explore how qualitative factors, such as regulatory environments and corporate governance, interact with quantitative network measures.

While the results of this study are robust, several methodological limitations must be acknowledged and their impact on the findings carefully considered. One major limitation is the sampling bias introduced by relying solely on publicly listed firms. This focus on larger, more established companies may have skewed the results by overestimating the influence of these central firms, potentially underrepresenting the role of smaller or privately held firms. In sectors where smaller firms play a critical role—such as energy—this exclusion could have masked key network dynamics, leading to a partial understanding of sectoral integration.

Moreover, the temporal scope of the study, covering data from 2013 to 2022, may not fully capture the long-term structural changes or cyclical patterns within these markets. While the selected timeframe offers valuable insights into recent trends in market integration, longer-term studies are needed to evaluate how these networks evolve over time, particularly in response to macroeconomic shocks or regulatory changes. As a result, the findings should be interpreted as reflecting a snapshot of emerging market dynamics rather than definitive long-term trends.

Another important limitation is the simplification introduced by the use of graph theory. While eigenvector centrality and Euclidean distance effectively quantify the interconnectedness and similarity of firms, these methods do not account for qualitative factors, such as corporate governance practices, political stability, or regulatory frameworks, which can significantly influence the behavior of firms and sectors. Future research could address these limitations by incorporating qualitative data or employing a mixed-methods approach to provide a more nuanced understanding of the forces shaping financial networks.

The findings of this study have practical implications for both policymakers and investors, offering actionable strategies to enhance financial stability and optimize investment portfolios. For policymakers, the identification of high-centrality firms provides a clear opportunity to target regulatory interventions that reinforce the stability of the financial system. By focusing on these firms, policymakers can mitigate the systemic risks associated with market fragmentation, particularly in sectors like energy and basic materials, which exhibited weaker network cohesion and higher volatility.

One concrete recommendation for policymakers is to strengthen the regulatory framework surrounding central firms, ensuring that they are adequately supported to continue acting as stabilizers within their sectors. This could involve incentivizing cross-sectoral collaboration, improving corporate governance standards, and enhancing market transparency. Additionally, policies aimed at encouraging innovation and investment in less central sectors could help to reduce market concentration and promote a more balanced distribution of influence within financial networks.

For investors, the identification of high-centrality firms presents a strategic advantage. These firms offer superior risk-adjusted returns, as evidenced by the 20% increase in profitability associated with central firms in sectors like telecommunications and retail. Investment strategies that prioritize sectors with strong network cohesion and focus on central firms can yield significant returns while also reducing exposure to market volatility. Investors could also benefit from a sectoral diversification strategy, targeting sectors like telecommunications and retail for their stability, while cautiously approaching sectors like energy, where higher fragmentation poses greater risks.

The findings of this study open several avenues for future research, particularly in understanding how financial networks in emerging markets evolve over time and under varying economic conditions. One key direction for future research is to explore the role of private and smaller firms within these networks. As this study focused on publicly listed firms, future research could incorporate a broader dataset that includes private entities, offering a more comprehensive view of sectoral dynamics. A key hypothesis for future exploration could be whether smaller firms, despite their size, exert a disproportionate influence in certain sectors and how their inclusion alters the network structure.

Another promising area of research is the non-linear dynamics of centrality during economic crises. Future studies could investigate whether high-centrality firms continue to stabilize markets during periods of economic stress or if their influence exacerbates market volatility. Additionally, cross-market comparisons between emerging and developed economies could yield valuable insights into how financial networks mature and whether the patterns observed in emerging markets hold true as these economies grow and stabilize.

Future research could also explore the interaction between institutional factors, such as regulatory frameworks, corporate governance, and political stability, and their impact on the financial network. Understanding how these qualitative factors shape the behavior of central firms could provide a more complete picture of market integration and suggest additional policy interventions to enhance market resilience.

Theoretically, this study advances the field of network theory by demonstrating the applicability of eigenvector centrality and Euclidean distance in assessing financial stability within emerging markets. By showing that central firms play a disproportionate role in stabilizing sectors, this study provides a critical contribution to the literature on financial networks, suggesting that the structural concentration of influence is a key feature of emerging markets. This insight challenges previous assumptions about market integration, which have often overlooked the unequal distribution of influence in less mature economies.

The integration of graph theory with financial analysis offers a multidimensional framework for understanding sectoral dynamics, highlighting the importance of both network position and financial similarity. This approach bridges the gap between quantitative network analysis and financial theory, suggesting that future studies could benefit from combining these methodologies to gain deeper insights into market behavior.

From a practical standpoint, this study provides actionable insights for investors and policymakers. The identification of key sectors and high-centrality firms offers a clear path for investment strategies and regulatory policies aimed at enhancing financial resilience. By focusing on the drivers of stability within these networks, stakeholders can make more informed decisions that promote long-term stability and economic growth in emerging markets.

6. BRICS Development Strategies

The BRICS nations—Brazil, Russia, India, China, and South Africa—have adopted multifaceted development strategies aimed at fostering economic growth, enhancing international cooperation, and strengthening their collective influence on the global stage. This section provides a comprehensive analysis of these strategies, elucidating their key components and impacts.

6.1. Economic Diversification and Industrialization

Economic diversification and industrialization are pivotal components of the BRICS nations’ development strategies, aimed at reducing dependency on primary commodities and fostering the growth of varied industrial sectors.

Brazil: Brazil has implemented policies to diversify its economy beyond agriculture and mining, significantly investing in manufacturing, technology, and renewable energy sectors. Initiatives such as the Plano Brasil Maior aim to enhance industrial productivity and innovation (Bastos 2012).

Russia: Russia’s strategy focuses on modernizing its industrial base and decreasing reliance on oil and gas exports. The government has introduced the Strategy for the Development of the Information Technology Industry to bolster the tech sector and enhance digital infrastructure (Ministry of Digital Development, Communications and Mass Media of the Russian Federation 2018).

India: India has launched the Make in India campaign to transform the country into a global manufacturing hub. This initiative seeks to attract foreign direct investment (FDI), develop infrastructure, and create jobs in sectors such as automotive, pharmaceuticals, and electronics (Government of India 2014).

China: China’s development strategy, articulated in the Made in China 2025 plan, focuses on upgrading its manufacturing capabilities and promoting high-tech industries, including robotics, aerospace, and clean energy (State Council of the People’s Republic of China 2015).

South Africa: South Africa’s Industrial Policy Action Plan (IPAP) aims to diversify the economy by promoting manufacturing, agro-processing, and green industries. This plan seeks to generate employment, increase exports, and foster sustainable development (Department of Trade and Industry, South Africa 2018).

6.2. Infrastructure Development

Infrastructure development is a critical element of BRICS strategies, supporting economic growth and regional integration.

Brazil: Brazil has invested in extensive infrastructure projects, including transportation networks, ports, and energy facilities. The Growth Acceleration Program (PAC) aims to improve logistics and energy infrastructure to enhance national competitiveness (Government of Brazil 2007).

Russia: Russia’s infrastructure development focuses on expanding transport networks, modernizing ports, and developing energy infrastructure. The Comprehensive Plan for the Modernization and Expansion of Core Infrastructure emphasizes connectivity and regional development (Government of the Russian Federation 2018).

India: India’s infrastructure strategy includes the development of smart cities, high-speed rail networks, and renewable energy projects. The Smart Cities Mission aims to create sustainable and efficient urban spaces (Government of India 2014).

China: China’s Belt and Road Initiative (BRI) is central to its infrastructure development strategy, aiming to enhance global trade connectivity through investments in transportation, energy, and telecommunications infrastructure across Asia, Europe, and Africa (National Development and Reform Commission, China 2015).

South Africa: South Africa’s National Infrastructure Plan focuses on developing transportation networks, energy projects, and water resources to address infrastructure deficits and promote economic growth.

6.3. Financial Cooperation and Institutional Development

The BRICS countries have established financial institutions and mechanisms to support their development goals and reduce dependence on traditional Western financial systems.

New Development Bank (NDB): Established in 2015, the NDB provides funding for infrastructure and sustainable development projects in BRICS and other emerging economies. The bank aims to complement existing financial institutions and foster financial stability (New Development Bank 2015).

Contingent Reserve Arrangement (CRA): The CRA is designed to provide financial support to BRICS countries facing balance-of-payments difficulties, serving as a precautionary measure against global financial volatility (BRICS 2014).

6.4. Technological Innovation and Digital Economy

Promoting technological innovation and the digital economy is a critical focus for BRICS countries, aiming to enhance competitiveness and drive sustainable growth.

Brazil: Brazil’s National Innovation Strategy emphasizes the development of high-tech industries, digital transformation, and research and development (R&D) initiatives to foster innovation (Ministry of Science, Technology and Innovation, Brazil 2020).

Russia: Russia’s Digital Economy Program aims to create a robust digital infrastructure, enhance cybersecurity, and promote digital literacy, positioning Russia as a leader in the global digital economy (Government of Russia 2017).

India: India’s Digital India initiative focuses on digital infrastructure development, improving internet connectivity, and promoting digital literacy to transform India into a knowledge-based economy (Government of India 2014).

China: China’s innovation-driven development strategy includes significant investments in R&D, artificial intelligence, and emerging technologies, aiming to lead global technological advancements and establish itself as a major innovation hub (State Council of the People’s Republic of China 2017).

South Africa: South Africa’s National Development Plan emphasizes innovation and technology as drivers of economic growth, including initiatives to support R&D, digital infrastructure, and skills development (National Planning Commission, South Africa 2012).