It all started ninety years ago as a story and now it is a reality
Graph theory is based on a system of vertices and edges that allow various elements to be linked or connected in order to be able to study the interrelationships that exist between them and the way in which they do so. For example, it allows us to know the possibility that exists of connecting two people among the almost 7,700 million human beings that populate the planet.
This theory would have been unthinkable to develop in ancient Greece or in the Middle Ages since at that time the social contacts that a person had were very few and the possibilities of traveling between two distant points were truly difficult. Such a theory could only be formulated in a globalized world, in which trains, ships, planes, and telephones were a reality.
A small world
It all started in 1930 when Hungarian writer Frigyes Karinthy proposed the ‘Six Degrees of separation theory in a short story called ‘Chains’. There it is reported that anyone on the planet can access another in just six steps or connections.
This hypothesis is based on the fact that the number of acquaintances a person has ranges between 50 and 100, and that it grows exponentially with each link in the chain. The weak point of this theory, at least on paper, is that several people can have acquaintances in common, with which the number of possibilities decreases.
In the 1950s the theory passed from literature to mathematics. The American sociologist Ithiel de Sola Pool (1917-1984) and the Austrian mathematician Manfred Kochen (1928-1989) formulated it in the following way: «What is the probability that, given a set of N people, each of its members is connected to another member via k1, k2, k3… with links?”. Unfortunately, they couldn’t make it to the demo.
In the following decade, psychologist Stanley Milgram (1933-1984) devised a simple method capable of testing this theory. This Harvard University professor designed a technique known as the “small world method”, which basically consisted of giving letters to hundreds of randomly chosen people and sending them to a single person – a New York stockbroker. -. Milgram just formulated a strange rule: letters could only be sent to the final addressee or to someone they knew and who might know them. If the second person knew the addressee, they sent the letter to be returned to Milgram, otherwise, they sent it to a third party who might know the stockbroker, and so on.
Against all odds, the packages arrived with a low number of links: between 5 and 7. In this way, the recipient and the sender seemed to be united by the famous “six degrees of separation”.
What if it was just four degrees?
Connectivity has increased in recent decades thanks to the internet and there are many who already defend that any person on the planet can be related to another in just four degrees. One of those who defend this theory is Mark Zuckerberg.
In 2011, through the ‘Anatomy of Facebook’ study, the friends of the 721 million users who were on that social network at that time and who represented 10% of the world’s population were investigated to see their degree of connectivity. It was found that 99.5% of users connected with only five degrees of separation.
Five years later the experiment was repeated, on that occasion, the number of users rose to 1,600 million and connection degrees fell to 4.5.
In 2013 Belgian Michiel Das, unemployed and despondent decided to put into practice the theory of the six degrees to find work in the city of Barcelona. He created just three business cards and gave them to three different people who he asked to pass them around until they reached a person who was willing to hire him. Which it was the result? After passing through the hands of four contacts, Das managed to get the marketing area of the Seat company to notice him and hire him.