The well-known saying ‘the enemy of my enemy is my friend’ is a part of the social balance theory developed by Austrian psychologist Fritz Heider in the 1940s. Previous attempts to create models of social networks based on this theory have been controversial. However, a new model has been developed that takes into consideration two key factors: not everyone in a social network knows each other, and some people are more friendly than others. When these factors are considered, large-scale social networks consistently align with the social balance theory. This model has wide-ranging applications in exploring political polarization, neural networks, drug interactions, and more. <p id= “first” class=”lead”>The famous phrase “the enemy of my enemy is my friend” is well known to most people.
Northwestern University researchers have used statistical physics to validate the theory behind this well-known saying.
Their study is set to be published on May 3 in the journal Science Advances.
In the 1940s, Austrian psychologist Fritz Heider introduced social balance theory, which explains how humans instinctively seek harmony within their social circles. According to the theory, there are four rules — an enemy of an enemy is a friend, a friend of a friend is a friend, a friend of an enemy is anenemy and, ultimately, an enemy of a friend is also an enemy — leading to balanced relationships.
Despite numerous attempts to validate this theory through network science and mathematics, studies have been unsuccessful as networks do not adhere to perfectly balanced relationships. Therefore, the crucial inquiry is whether social networks exhibit more balance than anticipated according to an appropriate network model. Many network models have been too basic to comprehensively encompass the intricacies of human relationships that impact social balance, resulting in inconclusive findings on whether observed deviations from network model expectations align with human behavior.The Northwestern team has successfully combined the two main components of Heider’s social framework, which has been a challenge for researchers. In real life, not everyone is acquainted with each other and people have varying degrees of positivity. Previous models could only address one of these factors, but the team’s new network model can accommodate both at the same time, finally confirming Heider’s theory nearly 80 years after its inception. This new framework can provide valuable insights into social dynamics for researchers.We have always believed that social intuition is effective, but we did not understand the underlying reasons for its effectiveness,” stated István Kovács, the senior author of the study at Northwestern University. “All we had to do was decipher the mathematics behind it. Despite numerous studies on the theory, there is no consensus among them. We have been mistaken for decades because real-life situations are complex. It became evident that we need to understand the interactions between positive and negative components in various systems, including political polarization and international relations, as well as neural networks or drug combinations.The study’s findings suggest that social networks align with expectations that were formed 80 years ago. This is significant because it means that the mathematics used in the study can be applied to model other systems beyond social networks. The study also takes into consideration the constraints on connections and the preference of different entities in the system. Bingjie Hao, the study’s first author, highlighted the importance of incorporating these constraints, stating that it will be useful for future applications. Kovács, an assistant professor of Physics and Astronomy at Northwestern’s Weinberg College of Arts, also emphasized the broad implications of the study’s findings.
nd Sciences. Hao is a postdoctoral researcher in his laboratory.
What is social balance theory?
Using groups of three people, Heider’s social balance theory maintains the assumption that humans strive for comfortable, harmonious relationships. In balanced relationships, all people like each other. Or, if one person dislikes two people, those two are friends. Imbalanced relationships exist when all three people dislike each other, or one person likes two people who dislike each other, leading to anxiety and tension. Studying such frustrated systems led to the 2021 Nobel Prize in physics to Italian theoretical phy
Physicist Giorgio Parisi was awarded the prize along with climate scientists Syukuro Manabe and Klaus Hasselmann. Kovács explained that the concept aligns with social intuition and can lead to extreme polarization, as seen in today’s political landscape. The difficulty lies in gathering large-scale data that includes both friends and enemies. Researchers have attempted to use Big Data to analyze signed data from social networks to understand this phenomenon.Confirming Heider’s theory involves creating networks to test his rules with individual people as nodes and the edges connecting nodes representing the relationships among individuals. If the nodes are not friends, then the edge between them is given a negative value, while if the nodes are friends, the edge is given a positive value. Previous models did not respect these constraints, assigning positive or negative values at random, which did not accurately capture the realities of social networks.Kovács and Hao used four large-scale signed network datasets collected by social scientists to study the problem. The datasets included user-rated comments on Slashdot, exchanges among Congressional members on the House floor, interactions among Bitcoin traders, and product reviews from Epinions. Instead of assigning truly random negative or positive values to the edges in their network model, the researchers recognized that every interaction can’t be random in real life. This is because in reality, every node doesn’t have an equal chance of encountering one another., not everyone is acquainted with every individual in their social network. For instance, a person may never come across a friend of their friend who resides on the opposite side of the globe.
In order to enhance the realism of their model, Kovács and Hao assigned positive or negative values using a statistical model that outlines the likelihood of assigning positive or negative signs to the existing interactions. This approach ensured that the values were random, but within the limits imposed by the constraints of the network topology. Apart from determining who knows whom, the team also considered that certain individuals are naturally more affable than others. These friendly individuals aremore likely to have more positive — and fewer hostile — interactions. By introducing these two constraints, the resulting model indicated that large-scale social networks consistently align with Heider’s social balance theory. Additionally, the model revealed patterns beyond three nodes, demonstrating that social balance theory applies to larger graphlets involving four or more nodes. According to Kovács, “We now know that these two constraints must be taken into account. Without them, the correct mechanisms cannot be determined. Although it may appear complex, it actually involves fairly simple mathematics.”
into polarization and beyond
Kovács and Hao are currently considering various future possibilities for this project. One potential direction involves using the new model to investigate ways to decrease political polarization. However, the researchers believe that the model could also be beneficial in understanding systems that extend beyond social groups and relationships between friends.
“We could examine the stimulating and inhibitory connections between neurons in the brain, or interactions that represent different combinations of drugs for treating illness,” explained Kovács. “Although the social network study was a great starting point for exploration, our primary focus is to expand our research into other areas.”The article “Proper network randomization is key to assessing social balance” explores interactions among friends and other complex networks.
