Physics has confirmed the age-old saying ‘the enemy of my enemy is, my friend’

Most of us have heard the saying, "the enemy of my enemy is my friend." This concept, deeply rooted in human intuition, has now found validation through the lens of statistical physics.

Researchers at Northwestern University have confirmed this age-old idea, providing fresh insights into social dynamics that could extend well beyond interpersonal relationships.

In the 1940s, Austrian psychologist Fritz Heider introduced the concept of social balance theory. This theory is built on the idea that humans naturally seek harmony in their social circles. According to Heider, relationships are balanced when:

These four rules are thought to guide human interactions towards balanced relationships. For instance, if three people are involved, balance is achieved if all three either like each other or if two people dislike a third, but like each other. Imbalance, on the other hand, leads to tension, as seen when all three people dislike each other or when one person likes two others who dislike each other.

The theory posits that balanced relationships are less stressful and more stable. While this idea aligns with common sense, previous attempts to confirm it scientifically have faced challenges, primarily due to the complexity of human relationships and the limitations of existing network models.

For decades, researchers have tried to validate Heider's theory using network science and mathematics. They mapped social interactions onto networks where individuals are represented as nodes, and their relationships as edges connecting these nodes.

Positive edges denote friendly relationships, while negative edges indicate hostility. However, many early models assigned these positive and negative values randomly, without considering the real-life nuances of social networks.

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As a result, these models often failed to capture the complexities of human interactions. Real-world networks rarely exhibit perfect balance, and the question remained whether these deviations from balance were consistent with Heider's theory or merely artifacts of oversimplified models.

Northwestern's team approached this problem with a fresh perspective, incorporating factors previously overlooked. They acknowledged that not everyone within a network knows each other and that some people are inherently more positive or friendly than others. By integrating these two factors, they created a more realistic model that aligns with Heider's predictions.

The new study, published in Science Advances, marks a significant step forward. István Kovács, an assistant professor of Physics and Astronomy at Northwestern, and Bingjie Hao, a postdoctoral researcher, led the research. Their work successfully combines both the likelihood of people knowing each other and their inherent positivity into a single framework.

“We have always thought this social intuition works, but we didn’t know why it worked,” Kovács explained. “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.”

To develop their model, Kovács and Hao examined four large-scale datasets, including:

Instead of assigning relationship values randomly, they used statistical models to distribute positive and negative signs in a manner that reflects real-world probabilities. This approach kept the interactions random but constrained within the network's topology, reflecting the true structure of social connections.

By considering these constraints, Kovács and Hao's model demonstrated that large-scale social networks do conform to Heider's social balance theory. Their work shows that balanced relationships are not just a theoretical construct but a reality in complex social networks.

This discovery extends beyond simple interactions among three individuals. The model also applies to larger groups, indicating that social balance theory can govern more extensive social structures involving four or more nodes.

Kovács emphasized the simplicity behind their approach: “We know now that you need to take into account these two constraints. Without those, you cannot come up with the right mechanisms. It looks complicated, but it’s actually fairly simple mathematics.”

The implications of this research are vast. Understanding social balance could provide insights into political polarization and international relations. As social dynamics become increasingly complex, this model could help explain how groups form and interact, potentially guiding strategies to reduce division and conflict.

Bingjie Hao noted, “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.”

One potential application is in the realm of political science, where the model could be used to study interventions aimed at reducing polarization. By understanding how social balance works, policymakers might design more effective strategies to foster unity and collaboration across divided groups.

Beyond social networks, the model could apply to various systems with positive and negative interactions. For example, researchers could study neural networks, where excitatory and inhibitory connections shape brain function. Similarly, the model could help in understanding drug interactions, where combinations of medications can have synergistic or antagonistic effects.

Kovács and Hao are excited about these possibilities and are already exploring new directions. “We could look at excitatory and inhibitory connections between neurons in the brain or interactions representing different combinations of drugs to treat disease,” Kovács said. “The social network study was an ideal playground to explore, but our main interest is to go beyond investigating interactions among friends and look at other complex networks.”

Northwestern University's breakthrough provides a new lens through which to view social interactions. By validating Heider's social balance theory with advanced modeling, Kovács and Hao have not only confirmed a long-held belief but also opened doors to understanding complex systems far beyond human relationships.

As we continue to explore the intricate web of connections that define our world, this research offers a crucial tool for unraveling the patterns that govern them.

Note: Materials provided above by Frontiers. Content may be edited for style and length.

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