Six-Degree Separation: Oh, What a Small World

Author(s): Abhijith S Babu

Originally published on Towards AI.

Recently, I was on a train journey from Kochi to Bangalore. On the train, I met a middle-aged man who was also on his way to Bangalore. We had a nice conversation, where he mentioned that his son studied electrical engineering at MECS College. That is where my cousin-brother studied the same course. I asked for more details about his son and texted my cousin-brother. And guess what?? They both were best friends in college. We were just two random passengers on a train boarding from faraway stations, and we still had a very close connection. What a small world, as it is usually said.

This close connection between people was found interesting years back, in the 1960s, when a psychologist from Harvard University conducted an experiment to show how closely connected people in the USA are, despite being a largely populated country. In the experiment, a set of 160 random people were selected from Omaha and were asked to pass on a message to a particular target person in Boston. The message can be passed on only to an acquaintance. Out of the 160 chains of messages that started in Omaha, 44 of them reached the target person in Boston, while 126 of them lost their path.

Let us assume that most of the chains that got lost were due to non-cooperation from the participants. Of the 44 chains that reached the target, the maximum length of the chain was 10, i.e., the message took a maximum of 10 people to reach the target. And the average length of the chain was calculated to be 5.5 people. Thus, the psychologist concluded that there is an average of 6 degrees of separation between any two random people.

We might doubt that this experiment is not sufficient to prove the six degrees of separation. But here, the participants are normal people who were free to pass the message to anyone they liked. They might not choose the optimal person to continue the chain. We can assume that the person chose the best recipient according to his knowledge, but that doesn’t guarantee that it is the best path.

Suppose I want to connect with a random Indian chef who works in Sweden. All the chefs that I know are local, and there is very less chance they might know a chef who has worked in Sweden for a long time. But my friend from school works in a bookstore in Sweden. So, for me, it is better to connect with him first. But it turns out that the chef I am trying to connect with is the first cousin of my gym trainer. If I connected through him, I could have reached my target in 2 steps, but since I had no idea about this connection, it took me a chain of 7 people to finally reach the target.

Similar experiments have been conducted in various parts of the world since then, even using Internet-based media. The analysis of how the chain progressed in the experiment gave some interesting insights. In the earlier steps, the participant is likely to choose the next recipient according to the location of the target person. As the chain grows, the participants choose to forward the message based on the occupation of the target person.

Some other factors also play a role in choosing a person. A participant is likely to choose the next recipient who probably cooperates and continues the experiment. The gender of the participant also played a role. A participant is more likely to choose a person of the same gender as his next recipient.

A small world network is a model in which many closely connected groups exist in the fully connected world. In that world, every member would be connected only to a small cluster of members, but some inter-cluster connections will make short paths between any two random members in the network. This nature is very well depicted in the film industry, where certain people almost always work together in movies.

Kevin Bacon game is a popular game in the film industry. A movie network is created from the data available in Internet Movie Database. Two actors are connected if they have worked in a common movie. The objective of the game is to find the shortest path in the network for a given actor from Kevin Bacon, called the Bacon number. The movie network contains as many as 248243 nodes. Even though the network is not fully connected, there is a fully connected partition of the network with 225226 nodes that contains Kevin Bacon. The Bacon number of the 225225 other members takes a maximum of 8. More interestingly, 80% of them are connected to Kevin Bacon in 3 or fewer connections.

The promising results from the Bacon game don’t show that Bacon is the central point of the movie network. Using various centrality measures, we have found other actors have more centrality than Kevin Bacon. The small world property of the world is the hero that made such unbelievable connections. It brings the world a lot together.

Everyone in the world is closer. You are separated from anyone else in the world only by an average of six people. Be it the president of the USA, Cristiano Ronaldo, or Dalai Lama. It doesn’t even have to be a famous person. A cab driver on your unexpected trip to Pretoria or a policeman in Ireland will also be separated from you by a small number of people. The small world feature doesn’t just apply to people, it can be found in other systems as well. It is a thing worth thinking about.

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Published via Towards AI