The search for balance in social networks
If you’ve ever tried to stay friends with both members of a couple going through a tumultuous divorce, or if you’ve hung out with a group of friends that includes someone you can’t stand, you know how unbalanced a social network can be.
You will likely also understand the 20th-century social psychologist, Fritz Heider, who theorized that humans seek to avoid these uncomfortable and unbalanced situations, preferring “balanced” networks that obey rules such as “the friend of my friend is also my friend” and “the enemy of my enemy is my friend.”
The difficulty of finding balance in social networks
However, it turns out that finding balance in real-world social networks is more complicated than it seems. Some studies suggest that social networks are balanced, while others assert the opposite. Moreover, some “null models” used to assess the statistical significance of observed patterns in real networks fail to identify balance even in artificial networks designed expressly to have it.
The discovery by physicists
Two physicists from Northwestern University in the United States recently announced that they had solved this problem. Using data collected from Bitcoin exchange platforms, the tech news site Slashdot, a product review site called Epinions, and interactions among members of the U.S. House of Representatives, István Kovács and Bingjie Hao showed that most social networks do indeed display strong balance. They claim that their discovery could be a first step toward “understanding and potentially reducing polarization in social media” and could also have applications in brain connectivity and protein-protein interactions.
Positive and negative signs in social networks
From a mathematical perspective, social networks are groups of nodes (representing people) connected by lines or edges (representing relationships between them). If two people have a hostile or mistrustful relationship, the edge connecting their nodes carries a negative sign. Friendly or trusting relationships receive a positive sign.
Factors complicating the balance of social networks
However, real-world social networks contain some subtleties that are difficult to capture in null models. For instance, not everyone knows each other mutually. If your enemy’s enemy lives abroad, for example, you may not know they exist, let alone whether to consider them a friend. Another complicating factor is that some people are friendlier than others, so they will have more positive connections.
The response of the physicists
In their study published in the journal Science Advances, Kovács and Hao created a new null model that preserves both the topology (i.e., the structure of connections) and the “signed node degree” (i.e., the friendship or hostility of individual nodes) that characterize real-world networks. By comparing this model to mini-networks of three and four nodes in their chosen datasets, they showed that real-world networks are indeed more balanced than would be expected based on the more accurate null model.
Conclusion: Can we really make friends by using our enemies?
Thus, the next time you have to choose between two arguing friends or decide whether you can trust someone who doesn’t like the same people as you do, rest assured: you are performing a simple mathematical operation, and the most likely outcome will be a more balanced social network. Problem solved!
