SIX DEGREES OF EMERGENCE.

Why does the six degrees of separation hypothesis hold up?

A recent paper published in Physical Review X by researchers from Israel, Spain, Italy, Russia, Slovenia, and Chile sheds light on the mechanism behind this phenomenon. It all comes down to human behavior and the constant balance between the costs and benefits of establishing new social ties.

If we might be able to understand all of the universe as a mathematical expression, should it come as any surprise that there isn't a mathematical economics of the universe?

People naturally seek prominence in social networks, strategically choosing connections that place them in central positions. However, forging new friendships requires effort and maintenance, which comes with a cost. So, individuals in social networks constantly play the cost-benefit game, breaking old ties and forming new ones to achieve an equilibrium that balances their desire for prominence and their limited social budget.

“When we did the math, we discovered an amazing result: this process always ends with social paths centered around the number six. Each individual acts independently without knowing the network as a whole, yet this self-driven game shapes the structure of the entire network, leading to the small world phenomenon and the recurring pattern of six degrees,” lead author Baruch Barzel, a professor at Bar-Ilan University, explains in a statement.

I bet when you look more carefully at the network, you're going to see a power rule in the links to some nodes.

Betweenness centrality essentially gauges how essential a node (or person) is in facilitating connections between other nodes. Imagine you’re friends with both a filmmaker and a film critic you’re central in the connection between these two people. The study adds an innovative twist to this measure by considering the “length” of the path through which an individual connects others, thereby giving a weighted importance to more direct connections.

‘Within this game, every agent continually evaluates whether forming new connections will improve their network influence or if maintaining existing connections is more beneficial. They make these decisions based on a balance between the associated costs and the projected benefits, aiming to maximize their influence within the network.

There might be strategies to add or remove people from your Rolodex, er, network, and yet, there is logic to the emergence of those six degrees.

When the game reaches a point where no individual has anything to gain by changing their existing connections—a situation known as Nash equilibrium—the resulting network naturally exhibits the characteristic of six degrees of separation. This means that any two people in the network could be connected through six or fewer intermediaries, offering a solid explanation for the phenomenon that has intrigued social scientists and the general public alike.

A Nash equilibrium is not necessarily a Pareto optimum, and yet, interacting agents are being led as if by an invisible hand into a network with those six degrees of separation.