One person might befriend another because of a shared love of basket weaving. Or, a friendship may instead blossom because that new friend has divergent interests, and can teach the other new hobbies. These opposing factors—seeking similarities and differences in relationships—are both crucial for explaining why and how people connect with one another. And both underlie a new model for how social networks form, published recently in Nature Communications. The model could be useful in understanding networks in society, biology, and finance. In particular, it can be used to design more productive cities with less crime, says coauthor Alex Pentland, a computer scientist at MIT.
Commonalities drive many relationships, and they’re the basis for many models of social networks, especially in sociology, Pentland says. They help explain societal phenomena such as all kinds of segregation and “echo chambers” observed in online and real-life networks.
But while a similar person might be easier to talk to, a dissimilar person could offer new opportunities and ideas—a motivation that drives most models in economics, Pentland notes. In these economic models, which are based on how a person benefits from a relationship, people favor a diverse social network.
Sociologists and economists thus offer contrary perspectives, he says. “Clearly they’re both right,” Pentland offers. “But they’re ignoring each other.” So Pentland, Yuan Yuan of MIT, and Ahmad Alabdulkareem of the King Abdulaziz City for Science and Technology in Saudi Arabia used techniques in machine learning and game theory to build a computational model of a social network that incorporates these two competing forces.
The model describes each individual with a set of initially unknown attributes. To determine whether two people are likely to befriend each other, the model weighs the costs and benefits of friendship by comparing those attributes. When the model is applied to a real social network, the attributes represent people’s similarities and differences. The model can identify which people must be similar or different in order to reproduce the observed patterns of that social network, such as who talks to whom in a network of phone calls.
Indeed, the researchers applied the model to phone calls among people in the country of Andorra (MIT has an agreement to access that nation’s phone records), as well as to movie directors and actors who worked together, employees in a company, trade interactions among countries, and a group of buyers and sellers.
Crucially, the model can uncover the similarities and differences of individuals based on the patterns of these networks—without any other information on the network’s content, Pentland says. “These two effects of an exchange of benefit and difficulty of communication, which are in opposition to each other, are likely the fundamental things that drive a lot of the patterns of interaction we see in society,” he adds.
Part of the model’s novelty is the ability to explain why connections are made, says Scott Page, a complex systems researcher at the University of Michigan. Modeling a network of disparate individuals is complex, often requiring machine-learning approaches. Although they can describe a network well, they do so in abstract terms that are difficult to interpret in the context of the real world. “What’s beautiful about this paper,” Page says, “is they’re trying to give you a way where, if I see this social network, can I infer back a set of benefits and a set of costs associated with each person—which is super cool.”
Moreover, Pentland says, the model can be used to predict how these costs and benefits offset, which can then inform policy. For example, a city is a network of people and places connected by lines of transportation. The model can show how reducing the costs of using that transportation—say, by improving bus lines and subways—can encourage mingling and increase diversity. And areas with little racial, socio-economic, and other forms diversity, as Pentland and others have shown in previous research, are linked to lower economic productivity and higher crime rates. “Similarity makes communication much easier,” Pentland says. “Diversity raises opportunity. You have to balance the two to get a healthy society.”
The new model isn’t without potential blindspots, however. These kinds of computational models may not provide as much insight as a mathematical one that can be solved exactly with pencil and paper, says Neil Johnson, a physicist at George Washington University in Washington DC. While exact models may be cruder, they can describe networks of any size. A computer would need to revisit a computational model to see if its behaviors remain the same for a larger network.
Another limitation is that the new model doesn’t account for who your friends’ friends are, says Matthew Jackson, an economist at Stanford. If you’re hunting for a business opportunity, for instance, a well-connected friend could be especially useful.
But Jackson does see value. “We’re in a time where networks are being changed more dramatically by technology than ever before,” Jackson says. “As a result, it’s very important to understand how they’re forming. These are big heterogeneous networks, so we need techniques like this to address those kinds of questions.”