Scheduled for publication in Science Advances on May 3, the study revisits social balance theory, first posited by Austrian psychologist Fritz Heider in the 1940s. This theory posits four fundamental rules for social harmony: an enemy of an enemy is a friend, a friend of a friend is a friend, a friend of an enemy is an enemy, and an enemy of a friend is an enemy. These rules, Heider suggested, dictate the balance in human relationships.
Despite numerous attempts to validate social balance theory using network science and mathematics, previous efforts often yielded inconclusive results due to overly simplistic network models that failed to capture the complex dynamics of human relationships. However, the Northwestern team successfully integrated necessary real-life factors-namely, that not everyone knows each other and varying degrees of positivity among individuals-into their network models, which allowed them to finally confirm Heider’s theory.
We have always thought this social intuition works, but we didn’t know why it worked, said Northwestern’s Istvan Kovacs, the study’s senior author. All we needed was to figure out the math. If you look through the literature, there are many studies on the theory, but there’s no agreement among them. For decades, we kept getting it wrong. The reason is because real life is complicated. We realized that we needed to take into account both constraints simultaneously: who knows whom and that some people are just friendlier than others.
Bingjie Hao, a postdoctoral researcher and the first author of the study, added, We can finally conclude that social networks align with expectations that were formed 80 years ago. Our findings also have broad applications for future use. Our mathematics allows us to incorporate constraints on the connections and the preference of different entities in the system. That will be useful for modeling other systems beyond social networks.
Kovacs and Hao used data from multiple large-scale signed network datasets, such as interactions on Slashdot, dialogues among Congressional members, Bitcoin trader interactions, and consumer reviews on Epinions. Their findings showed that these networks tend to follow Heider’s rules, suggesting that social balance applies not only to smaller groups but also across broader social networks.
This model not only validates long-held sociological theories but also opens new pathways for understanding complex systems, whether they involve human interactions or biological and chemical networks, Kovacs said.
The researchers are now exploring potential applications of their model in reducing political polarization and enhancing the understanding of other complex systems.
The code and data behind the paper, Proper network randomization is key to assessing social balance, are available on Github here.
