Signed networks model enhances understanding of global conflicts and alliances

• Researchers at IFISC and the University of Milano-Bicocca develop a model using signed networks to understand international relations.
• The study, published in the Journal of Applied Mathematics and Computing, proposes a local balance index to evaluate countries' contributions to global stability.
• The research analyzes historical data from 1816 to 2014, detecting significant geopolitical events based on balance fluctuations. 

Researchers from the Institute of Cross-Disciplinary Physics and Complex Systems (IFISC, UIB-CSIC), along with a colleague from the University of Milano-Bicocca, have introduced a new method to detect major historical events using network theory. Their study, published in the Journal of Applied Mathematics and Computing, leverages time-evolving signed networks to analyze international relations over a 200-year period, from the 19th to the 21st century. 

Understanding Signed Networks and Local Balance 

Signed networks are a mathematical representation where relationships are denoted as positive (e.g., alliances) or negative (e.g., conflicts). Traditionally, the concept of balance in these networks is evaluated globally. In contrast, this study introduces a local balance index, which quantifies how much a given node (or country) contributes to the global balance of the network. 

The study of signed networks has gained significant attention due to its applications in various fields such as ecology, biochemistry, sociology, and politics. Structural balance, the tendency of networks to avoid cycles with an odd number of negative edges, is a key property of these networks. While most empirical networks are rarely perfectly balanced, they often exhibit characteristics similar to balanced graphs. This has led researchers to develop indices that measure the level of balance. However, understanding which nodes (or countries) contribute more significantly to the network’s unbalance has been a challenging question. The local balance index addresses this by quantifying how much each country's relationships contribute to global stability, offering a new perspective on the stability and dynamics of international relations. 

Application to Historical International Relations

Using a historical database of alliances and conflicts from 1816 to 2014, the researchers constructed signed networks for each year and computed the local balance index for every country. The analysis showed that drops in the local balance time series are significantly correlated with the appearance of violent conflicts, while increases in local balance are correlated with non-violent events like peace treaties or the creation of supranational alliances. For example, the study identified a significant drop in the local balance index for France during the 1848 revolutions and a sharp decrease for Mexico during the Mexican Revolution, highlighting the index's sensitivity to historical upheavals. 

Statistical Validation and Broader Implications 

The researchers validated their model by comparing their results with historical records and geopolitical risk indices. The results demonstrated statistically significant correlations between fluctuations in the local balance metric and historical events recorded in historical databases. Furthermore, the study found strong correlations between the local balance index and the GeoPolitical Risk (GPR) index, which measures the frequency of newspaper articles discussing adverse geopolitical events. 

The research signifies a substantial step forward in network science and its application to international relations, showcasing the power of mathematical models in deciphering complex social systems. This innovative approach opens new avenues for future research. By applying the local balance index to contemporary data, researchers can potentially predict emerging geopolitical tensions and shifts in international alliances. Furthermore, integrating this model with other quantitative methods could enhance our understanding of global stability and inform policy-making and diplomatic efforts.

Diaz-Diaz, F., Bartesaghi, P. & Estrada, E. Mathematical modeling of local balance in signed networks and its applications to global international analysis. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02204-2

• El Diari de la UIB