Your Enemy's Enemy Really Is Your Friend - According To Physics!

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Statistical physics has been used to corroborate social balance theory.

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Hating someone is also a great way to bond!

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Humans are social animals whose web of relationships is convoluted and often changing. Understanding these social networks and their changes has been the remit of different sciences and various theories. One of them was proposed in the 1940s, called social balance theory. Now, researchers have been able to corroborate it using statistical physics.

The idea at the center of social balance theory is, as the name suggests, balance. Individuals want and try to keep balanced relationships within their networks. Positive relationships are balanced, while negative or mixed relationships are not, and you need rules to keep the system balanced. The classical model has four simple rules, based on the simplistic idea that positive relationships are "friends" and negative relationships are "enemies".

The first rule is that a friend of a friend is a friend. Now, this is an idealized case - do not immediately jump to thinking about that friend of your friend whom you hate. Another rule is a friend of an enemy is an enemy, and obviously the enemy of a friend is an enemy - we've got to defend our pals. The final rule is more subtle: an enemy of an enemy is a friend. The new analysis tends to agree with this requirement, but the scientists had to bring in significant complexity before they were able to model it.

"We can finally conclude that social networks align with expectations that were formed 80 years ago," first author Bingjie Hao, from Northwestern University, said in a statement. "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."

Crucial to the new model were two factors: not everyone knows everyone else in real life, and some people are more positive than others. Using both constraints actually reproduces a social network just like the one predicted by Fritz Heider 80 years ago.

"We have always thought this social intuition works, but we didn't know why it worked," added István Kovács, 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."

The study is published in the journal Science Advances.