What is a Line? - Chosen Concept

Six Degrees of Separation

This refers to the idea that everyone is on average approximately six steps away from any other person on Earth, so that a chain of, "a friend of a friend" statements can be made, on average, to connect any two people in six steps or fewer.

Social networking

Twitter
According to Sysomos, a social media analytics company, the average distance/steps between two Twitter users is 4.67. 50% of users are 4 steps away from each other whilst almost all are 5.

Facebook
A Facebook platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between different people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12. The application has a "Search for Connections" window to input any name of a Facebook user, to which it then shows the chain of connections. (This will be useful for my own research)

Wikipedia
Stephen Dolan, a student at Trinity College Dublin, applied graph theory to work out the "closeness" of an article in Wikipedia as its average distance to any other article, to find the "centre" of Wikipedia. Apart from dates (2007 being 3.45 clicks to 2,111,479 other articles), the "centre" is "United Kingdom", at an average of 3.67 clicks to anywhere else.

Maths

Watts and Strogatz showed that: Average Path Length = (ln N / ln K) where N = total nodes and K = acquaintances per node. Thus if N = 300,000,000 (90% US pop.) and K = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if N = 6,000,000,000 (90% World pop.) and K = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6. (Assume 10% of population is too young to participate.)