The 1995–2018 global evolution of the network of amicable and hostile relations among nation-states

The study of how relationships between countries—characterized by amity or hostility—evolve over time is a significant area of interdisciplinary research. Structural Balance Theory (SBT) provides a framework for understanding the dynamics of these signed appraisal networks, proposing that changes are driven by tensions created by intransitive relationships (e.g., a friend of a friend is not a friend). However, progress in this field has been hampered by a lack of large-scale, longitudinal data on international relations. This paper aims to address this limitation by analyzing a comprehensive dataset to test SBT's predictions and develop a model for the probabilistic evolution of international appraisals. The importance lies in the potential to improve understanding of conflict origins, alliance formation, and power balances, offering insights into international relations dynamics and potentially informing conflict prevention strategies.

Existing research on international relations has often drawn upon SBT, investigating the origins of major conflicts like World War I (Gellman et al., 1989; Antal et al., 2006) and the Bangladesh Liberation War (Moore, 1978). Harary et al. (1961) used SBT to analyze the Middle East crisis of 1956, showing how countries sought new equilibrium alignments after international shocks. However, these studies were often limited by data constraints, focusing on small populations or limited time spans. While SBT has found applications in various fields, from consumer branding (Woodside, 2004) to social animal behavior (Ilany et al., 2013), its dynamic predictions have rarely been thoroughly tested with extensive longitudinal data (Szell et al., 2010). Existing longitudinal studies have been confined to small populations or few temporal states (Zheng et al., 2015). This study addresses the need for large-scale, longitudinal analysis to better understand the dynamics of SBT in international relations.

This research uses the Integrated Crisis Early Warning System (ICEWS) dataset, a comprehensive, automated, and validated system for monitoring international crises (Shilliday & Lautenschlager, 2012). The dataset contains 8,073,921 international events spanning September 1, 1995, to September 30, 2018, involving 250 countries. Each event represents a positive or negative appraisal between two countries, with a value ranging from -10 (completely offensive) to +10 (completely supportive). The data includes positive, negative, and null (neutral) international relations. The data was analyzed by dividing it into time periods (e.g., three-month intervals). For each period, a network was constructed with countries as nodes and signed edges representing the aggregated appraisal between country pairs. The study then analyzed triad structures—groups of three countries—to assess structural balance according to various definitions (classical, clustering, transitivity) which generalize SBT to include null edges. The number of triad types possible is 138. The authors examine the proportion of balanced and unbalanced triads over time and analyze the transition probabilities between triad types using Markov models. A novel convex optimization model was developed to estimate the time-varying Markov chains and quantify the dynamic stability of the system. The authors further investigate the network's structure, identifying a core-periphery structure and examining the evolution of this structure over time. Additionally, the study analyzes the relationship between the stability of the network dynamics and exogenous factors such as large-scale international events and global trade activity. Granger causality tests were used to assess the causal relationships between global trade and the stability of international relations.

The study's empirical findings contradict the classical SBT prediction that networks of international relations will evolve towards either a fully positive network or a bipartite network of two antagonistic groups. Instead, the evolution is primarily driven by a reduction in intransitive relations, resulting in more complex network topologies. The analysis shows that a surprisingly small subset of the 138 possible triad types (only ten) account for 91% of observed triads over the 23-year period. While the proportion of balanced triads initially decreases before 2006, due to the increase in positive ties, it trends towards greater balance thereafter. Analysis of the Markov transition matrices reveals a high probability of transitioning from unbalanced to balanced triads, suggesting a dynamic towards structural balance. This trend is robust across different time period definitions (seasonal, monthly, bi-weekly, weekly). The time-varying Markov model confirmed the high probability of transitions to and from balanced states and high probabilities of balanced triads remaining balanced. The Frobenius norm of the sequential transition probabilities, indicating the stability of the system's dynamics, exhibits a dramatic stabilization over time, with disruptions correlating with significant international events (e.g., 9/11, the Iraq War). Furthermore, a strong negative correlation was found between the Frobenius norm difference of consecutive matrices and global trade activity (Pearson's correlation coefficient of -0.88, p < 1e-07). Granger causality tests showed a significant effect of global trade on the stability of the dynamics, suggesting a feedback loop where increased trade leads to greater stability and vice versa.

The findings suggest that SBT's core prediction—the tendency towards balance—is largely supported, even in large-scale networks with null relations. The initial decrease in structural balance is likely a consequence of increasing connectivity among countries, rather than a rejection of SBT. The transition to increased balance after 2006 supports the hypothesis that reductions in intransitive relations drive the evolution of international appraisals. The strong correlation between global trade and dynamic stability is consistent with prior research suggesting that increased trade reduces incentives for conflict (Jackson & Nei, 2015; Martin et al., 2008; Oneal & Russett, 1999; Hegre et al., 2010). The model's robustness across different time granularities and its generalization to other datasets (Bitcoin trust networks, supplementary information) suggest that the movement towards balance is a pervasive phenomenon in various types of signed networks.

This study provides significant empirical evidence on the dynamics of structural balance in large-scale international relations using a substantial longitudinal dataset. The findings support the core tenets of SBT, indicating a consistent trend towards balanced triads. A novel time-varying Markov model effectively captures the underlying dynamic stability, showcasing a strong correlation with global trade activity. Future research could explore non-Markovian models to improve predictive accuracy and investigate the influence of other factors beyond trade on the evolution of international relations.

While the ICEWS dataset is comprehensive, it may not capture all aspects of international relations, potentially leading to biases. The aggregation of events into single signed edges for each country pair in a given time period could mask the complexity of nuanced interactions. The study's focus on triad analysis might overlook higher-order network structures that could influence overall balance. Finally, the causal relationship between trade and stability is inferred through statistical correlations and Granger causality tests and should be investigated further.