Leaders in the global banking network: Analysis of the Bank for International Settlements network data Anthony Bonato; Juan Chavez Palan; Adam Szava PLOS One · 2025-10-31 CC BY 4.0 · https://creativecommons.org/licenses/by/4.0/ Source: https://doi.org/10.1371/journal.pone.0335506 Abstract Prior work on networks derived from the Bank for International Settlements (or BIS) focused on centrality measures such as degree, betweenness, and DebtRank, with less attention given to adversarial network models. In this work, we address this gap by introducing an adversarial network-based method to locate influential countries within the global banking network. We analyze BIS data from 2000 to 2015, modeling countries as nodes and lending relationships as weighted, directed edges. We study low-key leaders, which are countries with outsize influence despite lower centrality, and highly exposed nodes, which are countries most vulnerable to defaults. Using the Common Out-neighbor (or CON) score with PageRank, we quantify each country’s influence and exposure, and define a measure of low-key leader strength. Our results show that low-key leaders, such as those in the United States and Mexico, possess strong influence with lower exposure to contagion, whereas highly exposed leaders, like those in Germany and the United Kingdom after 2003, maintain broad lending portfolios that heighten vulnerability. We also examine these roles over time, including the United States’ loss of low-key leader status after the 2008 financial crisis. Our analysis of low-key leaders and highly-exposed nodes provides new insights into systemic risk within the BIS network. Introduction Networks play a central role in analyzing complex real-world systems, ranging from social interactions to financial transactions. In the context of global banking, network analysis offers powerful tools to uncover hidden patterns, assess systemic risks, and develop strategies for regulatory compliance. The interconnected nature of financial institutions implies that vulnerabilities in one part of the system can propagate, resulting in cascading effects throughout the network. The Bank for International Settlements (or BIS) provides consolidated data on cross-border banking relationships. For more background on BIS, see [1,2]. We can form a network using BIS data, where nodes represent countries and directed edges indicate cross-border lending relationships. The BIS network has been used to model risk contagion and identify critical nodes. For a discussion of network methods using BIS data focused on European markets, see [3]. In [4], in- and out-degree distributions were used to analyze consolidated and locational banking statistics in BIS data to measure resilience. In [5,6], degrees and betweenness centrality were used to analyze the global banking network, while [7] used betweenness and eigenvalue centrality. DebtRank, introduced in [8], is a recursive centrality measure used to estimate the impact of shocks in financial networks. DebtRank has been used to study shock propagation and resiliency in banking networks; see [9,10]. Centrality measures such as the Common Out-neighbor (or CON) score and PageRank have been used to detect alliances, leaders, and other influential nodes in adversarial or competition-based network models; see [11–13]. In this study, we analyze the BIS data using the framework of adversarial networks, which represent competitive and antagonistic relationships between nodes. Unlike the earlier studies described in the previous paragraph, we leverage centrality measures such as the CON score and PageRank to uncover two types of influential players: low-key leaders, whose influence is understated by traditional centrality measures, and highly-exposed nodes, which are particularly vulnerable to financial contagion. Our approach using adversarial networks is a novel one and provides insights into systemic vulnerabilities in the global banking system. Financial contagion in BIS data The Bank for International Settlements was founded in 1930 to facilitate reparations imposed on Germany after World War I. Reparation tasks became obsolete, and BIS became a provider of statistics and analysis that could aid the cooperation between central banks [2]. Due to globalization over the past century, there have been growing financial interdependencies between developed countries, which have given the BIS a renewed role. The BIS is now heavily involved whenever a financial crisis occurs, as it looks to recommend solutions to preserve financial stability [1]. The institution has expanded to 63 owner countries over the last three decades, becoming a meeting ground for regulators to pursue the standardization of banking practices and demand transparent reporting among the world’s major financial players [14]. Since the Latin American debt crisis of 1982, one of the topics of interest at the BIS has been the interdependencies within the global lending network; this refers to the worldwide debt held among banks from reporting countries. This dataset is publicly available and published by the BIS Committee on the Global Financial System (or CGFS). While its official purpose is to identify potential sources of stress in the global financial system, it can also be studied to track where a banking crisis in one country can lead to a cascade of defaults in other countries; see [4]. Previous studies conducted by Chen et al. explored financial contagion in the BIS network by sampling only 18 banking systems from this dataset; see [15]. We will extract graphs from the entire global set of 62 CGFS’s quarterly data reports from February 2000 to June 2015, modeling them as adversarial networks. Our goal will be to identify the presence of any low-key leaders and to determine if they play a significant role in the network’s susceptibility to financial contagion. The CGFS publishes two sets of international banking statistics every quarter. The first is for locational statistics, which is a set of financial statements with assets and liabilities from banks in each reporting country. This information can be significant in the study of a country’s internal financial stability. However, as we are concerned with the external interdependencies between countries, we omit locational statistics from our analysis. The second is a set of consolidated statistics, which sums up the accumulated debt from all banks within a country and reports this sum as a consolidated debt-by-country balance. For example, if Canadian banks have lent money through their head office or overseas branches to banks based in France, then the BIS collects the consolidated sum of debt that all French banks owe to all Canadian banks as a single amount. From a financial standpoint, this provides a direct measure of the risk exposure each country’s banking system has in an external crisis. To continue with our previous example, if the French banking system defaults, all Canadian banks with debt in French bonds would be exposed to the risk of defaulting on their obligations, potentially triggering a crisis in the Canadian banking system. Three types of consolidated statistics were published in the statistical annex of each BIS Quarterly Review. For our study, we will focus on the Foreign claims on an immediate borrower basis by BIS reporting country, which were reported during the 2000 to 2015 period as shown in Table 1. We chose this dataset for its simplicity. The table illustrates the amount of contractual debt held by one country’s banking system against another. This was done through their banks’ head offices and all their branches and subsidiaries worldwide on a consolidated basis, with any internal bank amounts subtracted. For example, if a bank in Canada has branches in multiple countries, any debt held by those foreign branches or subsidiaries will still be reported as debt held by the Canadian bank. This is because the head office entity in Canada would bear the losses in the case of a default. Any debt held by a Canadian branch located in France is considered internal within the Canadian bank’s financial statements. These are not to be counted as part of what debt France would owe Canada. The other two sets of consolidated data have been omitted from our analysis, as they include different attributes for risk mitigation, such as guarantees and collateral, which are tools to prevent the impact of defaults; these would add a higher level of complexity to the interpretations of our model and can be explored in future research. Adversarial networks. Adversarial networks are those in which edges model relationships involving competition, dominance, or enmity. We focus here on competition networks: if u is in direct competition with v, then the direction of the edge (u,v) represents a negative correlation, such as when u owes money to v. In [11,12], the authors developed a hypothesis that served as a predictive tool to uncover alliances and leaders within dynamic competition networks, where directed edges are added over discrete time steps. Consider a dynamic competition network G. For nodes u, v, w, we say that w is a common out-neighbor of u and v if (u,w) and (v,w) are two directed edges in G. Let CON(u,v) be the number of common out-neighbors of two distinct nodes u and v. The Common Out-neighbor (or CON) score of a fixed node u is defined as For a set of nodes S⊆V(G) with at least two nodes, we define: The CON centrality measure has been presented through multiple applications to dynamic competition networks in [11,12]. An influential node is expected to have engagements in sync with many others in the network; conversely, a non-influential node will have limited such interactions. In particular, a high CON score for a fixed node u indicates that it shares many of the same adversaries with other nodes. Hence, u will influence how the network evolves, if even indirectly. A low CON score indicates that a node does not share the same adversaries as other nodes, and therefore, it will not significantly impact the network’s evolution. The Dynamic Competition Hypothesis (or DCH) provides a quantitative framework for the structure of dynamic competition networks; see [11]. To apply this hypothesis to a banking network, we must first introduce the concepts of an alliance and a leader within a competitive network. Alliances are associations formed for mutual benefit, such as countries that pool resources to achieve a common goal. In [12], the authors study social game shows, such as Survivor, where alliances are groups of players who collaborate to vote out players outside the alliance. Leaders would be players with a high standing among their peers in the network, and outgoing edges from these leaders will influence edges (which are votes) created by other players. The DCH states that dynamic competition networks arising from an adversarial network satisfy the following properties: (1) Strong alliances have low edge density; (2) members of an alliance with high CON scores are more likely leaders; and (3) Leaders exhibit high closeness, high CON scores, low in-degree, and high out-degree. The DCH was tested against winners of social game shows, influential actors in political conflicts, and the hierarchical position of biological species in the food chain, as cited in [12]. The authors corroborated that alliances corresponded to nearly independent sets, that CON scores accurately determine the leaders of alliances, and that leaders are detected via their CON scores and closeness. A contrasting centrality measure for adversarial networks is the well-studied PageRank centrality measure, first introduced in [16]. For additional background on PageRank, see [17]. A high PageRank for a fixed node u in a directed graph will likely correlate with high in-degree nodes. This is why, for an adversarial network, we will compute the PageRank of nodes on a reversed-edge network. Therefore, a high PageRank in an adversarial network will correlate with a node that has a high out-degree. A low-key leader (or LKL) in an adversarial network is a node whose CON score and PageRank (reversed-edge) are negatively correlated, with a higher CON score and relatively low PageRank. LKLs were first discussed in [13]. Hence, an LKL node would still be influential in the network, but with less centrality than a traditional leader. To be able to calculate a difference between the two values, we note that CON-scores are positive integers and PageRank scores are probabilities, so we re-scale both scores by using unity-based normalization: This scaling measure will satisfy Xnorm∈[0,1] and can create a ranked order of nodes according to either their CON-score or PageRank. To help illustrate the concept, Fig 1 provides a toy example containing an LKL. In this network, node B has the highest CON score. However, in the reversed-edge network, A has the highest PageRank, and B has a relatively low PageRank, demonstrating that node B is an LKL. Let G be a directed graph, for the set of nodes vi∈V(G), where 1≤i≤n, and the CON-score and PageRank of vi are denoted by CONi and PRi, respectively, we define low-key leader strength as where ϵi∈[−1,1]. A node vL is a low-key leader if it has the maximum value of ϵL, and ϵL>c, where c is a parameter determined by the network. In selected sets of adversarial dominance within animal populations, cryptocurrency, and global trade networks, the authors in [13] identified low-key leaders as those with the highest values of ε, where ϵ>.5. Furthermore, it was demonstrated that low-key leaders are prevalent in most of the studied adversarial networks. Applications to BIS data. We obtained tables corresponding to BIS Quarterly Review reports from February 2000 to June 2015. See Table 1 for an example of a data extract that shows where each row corresponds to a debtor country, whose banking system owes money collectively to foreign lender countries’ banks. Each column corresponds to the reporting lender country that holds the debt and is owed this amount. We selected sets of adversarial dominance within the 62 adjacency matrices from the datasets. Each node v∈V(G) corresponds to a country, and each weighted directed edge (u,v;k)∈E(G) corresponds to the amount of money k that is owed by country u to the country v. The full dataset of adjacency matrices is available on the following GitHub page: https://github.com/AdamSzava/BISNetworkData. The directed edges (u,v;k) are inherent adversarial relationships, where each debt k from u to v is an adversarial obligation from a debtor to a lender counterparty. Graph G is also a dynamic competition network as it evolves. Each reporting lender country competes with the others to take advantage of new investment opportunities by forming alliances with outlier countries. Each debtor country competes with others to obtain additional foreign investment, while each reporting lender country competes to seize new opportunities by forming new alliances. We then compute the weighted CON score and PageRank of each node to calculate the low-key leader strength of all countries across the adjacency matrices. BIS data Countries with a high-weighted PageRank correlate with nodes that have a high-weighted out-degree. These are countries that owe significant amounts of money to reporting lender countries. As a result of their high centrality, these countries are heavily integrated in the event of a financial contagion and become crucial to the stability of the network. If any of these countries default, then there is a greater risk to the entire network. During the period we studied, Germany, the United Kingdom, and the United States alternated in having the highest PageRank values. Some of the results for March 2006 are shown in Table 2, where we can see that, although the United States owes the largest amount of debt across the network, it does not have the highest PageRank during that same period. A high PageRank also represents a higher likelihood that the random walk would visit the node at any given time. This has an indirect implication in our adversarial reversed-edge network. Whenever a country falls into default, it is more likely that it would have owed money to the country with the highest PageRank, or through transitivity, it could have owed money to a country that ultimately owes money to the country with the highest PageRank. Consequently, the country with the highest PageRank is at an increased risk of default from any random member of the network. Countries with a weighted high CON score tend to share similar debt obligations with other nodes; these countries owe large amounts of money to selected lender countries that most other nodes in the network also owe money to. Their debt is both large and diversified, as they share similar debt obligations as their neighboring nodes; hence, the actions of these countries can influence how the network evolves. A low CON score could indicate that a country does not owe a large amount of money and that any significant debt it owes might not be to the same countries that its neighbors owe money to. As seen in Table 3, which compares some results for March 2006, Germany has lent an amount of over $US 3 trillion at this point, which is three times as much as the United States has lent US one trillion, and slightly above the United Kingdom, who are owed US $2.5 trillion. This means that the network as a whole owes more money to Germany than to the United Kingdom or the United States on a consolidated basis, and countries with the highest CON scores are the most likely to owe this money to Germany. A high CON score gives a country the highest influence over causing a financial contagion if it falls into default. It is worth noting that the United States consistently ranks with the highest weighted CON score throughout the entire 2000-2015 period. Low-key and highly-exposed leaders in BIS. For the calculation of the low-key leader strength, we explored maximum values of ε and determined that the absolute maximum ϵ=0.6036 occurs for the United States in September 2005, as well as the relative minimum and maximum LKL strength values based on interquartile ranges oscillate from ±0.02 to ±0.08. Therefore, we determine that a low-key leader for the BIS network exists whenever there is an extremely positive LKL strength outlier such that ϵL>c, and c = 0.1. During a brief period from February 2000 to December 2001, a few countries met these criteria, including the United States and the United Kingdom, notably Italy and Ireland. Throughout the period from March 2002 until December 2010, the United States was the only low-key leader that surpassed this threshold. From March 2011 to June 2012, the United States and Mexico shared the status. Eventually, in September 2012, Mexico became the sole leader, a position it held until June 2015. Fig 2 shows the low-key leader strength during March 2006, when the United States was the only low-key leader. Being a low-key leader in the BIS network correlates with being one of the top lenders of money worldwide, although not necessarily the one with the greatest risk exposure at the very top. They could also have a smaller list of debtor countries than other top lenders. This country is one of the leaders sheltering itself from financial contagion by maintaining a lower level of integration. A relatively higher-weighted CON score ensures that they remain a top player with significant influence over the network’s evolution. The low-key leader owes large sums of money compared to other countries with similar PageRank, implying that they are the country that could cause the most damage if they were to default. An interesting phenomenon also occurs at the other end of the LKL strength graph. Multiple countries are meeting the reversed threshold ϵL<−c, as seen in Germany and Japan in Fig 2. This occurrence is not explored in the current literature, so we provide a possible interpretation of the significance of these nodes, which have a high-weighted PageRank and a relatively lower-weighted CON score. In an adversarial network, define a highly-exposed leader as one having a much higher PageRank than CON score. Hence, a highly-exposed leader has negative low-key leader strength, typically below some fixed threshold ϵ<0. We explored the minimum values of ε and determined that the absolute minimum, −0.7773, occurs for Germany in June 2002. While there is a consistent number of countries with ε values below -0.2, only a select few have values below -0.4 across the entire period. Therefore, we determine that a highly-exposed leader for the BIS network exists whenever there is an extremely negative LKL strength outlier such that ϵL