The Six Degrees of Separation theory

Do you know SixDegrees.com was the first social network site which allowed the user to create a profile and connect?

In a world of 7 billion people, it seems hard to believe that the Six Degrees of Separation theory contends that we are all connected to each other by six or fewer acquaintances.

For example, there are, at most, six people standing between you and Tom Cruise or President Obama (or Trump if you lean that way).

Going by the numbers, the idea looks pretty plausible.

Assume that you know 50 people or have 50 friends and these 50 friends of yours know 50 others who are not your friends, and so on.

The math says that in 6 steps you would be connected with 50⁶, or 15.62 billion people.

Six Degrees of Separation Theory 

In 1929, Hungarian author Frigyes Karinthy published a volume of short stories named Everything is Different.

In one of his stories titled Chains, he said that with growing communication and travel, the friendship network would grow irrespective of the distance between two humans.

And with a growing social network, the social distance would shrink immensely.

All the people on the planet could be connected to one another by 5 or fewer people.

This theory captivated millions of mathematicians, sociologists, and physicists and also laid the founding stone of the first online social network.

Soon several “small world” projects were conducted.

The small world experiment comprised experiments conducted by Stanley Milgram, examining the average path length for social networks of people in the United States.

These experiments suggested that humans are connected to each other through a network, connected to each other by the shortest path.

In 2005, Samy Kamkar wrote a small piece of code for his myspace account.

Whenever anyone visited Samy’s profile, it copied his picture and tag line on his home page saying “Samy is my hero” and also copied the code.

Within 20 hours, this code was on more than 1 million myspace user profiles. It is considered one of the fastest growing web viruses of all time.

Though mostly harmless, Samy was caught by the United States Secret Service and was prohibited from using the  Internet for three years.

The point I am trying to make is that within a span of few hours, a simple XSS webworm was shared among more than 1 million users, proving that the world was getting smaller and further studies and research on small world projects need to be escalated.

The real breakthrough came with the college game of “Six degrees of Kevin Bacon” where college students linked other Hollywood co-stars to Kevin Bacon in six or fewer steps.

The huge volume of data collected in the game gave scientists and researchers immense information to process and proceed and gave them opportunities to prove the concept of six degrees of separation.

You can check the game at Oracle of Bacon.

In 2011, Facebook and researchers at Cornell computed that the average separation across 721 million people using Facebook was only 3.74.

In their latest research published in February 2016, this number dropped down to 3.57, with more than 1.59 billion people active on Facebook.

On average, Facebook users are connected by an average of 2.9 to 4.2 degrees of separation. The image shows the average of each person.

Six Degrees of Separation Theory meaning analysis 

In its research paper, Facebook mentions that this estimation was done using the Flajolet–Martin algorithm, which is used to find distinct elements in a stream of elements.

Suppose you assign an integer called Hash to each friend in a group (Read more about Hash Function here).

Approximately half of your friends will have even numbers or even hash, whose binary representation would be 0.

A quarter of them would have the number divisible by 4, giving the binary representation as 00. This means ½ⁿ people will have their hash or numbers ending with n zeros.

To track, you find the number with the maximum number of zeros. If there are n zeros, you can find C*2ⁿ unique numbers.

To calculate the average, you find the number with the maximum number of zeroes.

Use Bitwise OR operation on these numbers and then recursively do it for one set of friends, and then friends-of-friends, and their friends and so on to find the shortest path.

The result is amazing! It is just unbelievable how small the world is.

With a growing social network, the average separation and connection would soon reduce to possibly 2 to 3 degrees of separation.

And someday, a mail from The Prince of Somalia telling you that you have won the lottery might be actually true!

Till then, connect with best developers across the planet using first degree connections by building your profile on HackerEarth and participating in various programming challenges.

Arpit Mishra Author 49 Blogs