“The average path length between two nodes in a random network is equal to ln N / ln K, where N = total nodes and K = acquaintances per node. Thus if N = 300,000,000 (90% of the US population) and K = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if N = 6,000,000,000 (90% of the World population) and K = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6. (Assume 10% of population is too young to participate.) (Watts, D.J.; Stogatz, S. H.).”
Yes, this is a formula to calculate the six degrees of separation averaging at 6.6. A ‘degree of separation’ is a measure of social distance between people. You are one degree away from everyone you know, two degrees away from everyone they know, and so on (theguardian). The Six Degrees of Separation is widely spread by pop culture but is it in fact true or just a myth?
Primetime set up an experiment with the University of Colombia to test if and how quickly random people could connect to a third individual. Sixty thousand people from one hundred-seventy countries took part in the experiment;the project was carried out online. In the experiment, each participant was assigned a random person around the world which they were to link via e-mail without directly emailing it to that person. Essentially, they were to connect by creating a human chain. To proceed the participant would e-mail someone they know then ask that person to continue the links by e-mailing someone else they know. The objective is to eventually send an e-mail to someone who knows the assigned person personally, completing the chain. Of the hundreds of chains that have been completed, the average number of links has been six, supporting the six degrees of separation theory (T.Berman abcnews).
Another study done by Microsoft showed similar results. In this study, Microsoft studied records of thirty billion electronic conversations among one hundred-eighty million people in various countries. The database covered all the Microsoft Messenger instant-messaging network in June 2006. Microsoft looked at the minimum chain lengths it would take to connect one hundred-eighty billion different pairs of users in the database and found the average length was 6.6 stages, and that seventy-eight percent of the pairs could be connected in seven steps or fewer (theguardian).
So is the six degrees of separation true? Mosty. Studies on average showed people were connected on average 6.6 degrees proving the formula and studies to be almost exactly six degrees and true.
http://www.theguardian.com/technology/2008/aug/03/internet.email