Finally, a proof that the world is small!

"The small-world e?ect and six degrees of separation were then con?rmed on a truly global scale. The average distance between vertices of the giant component was found to be 4.7, and we interpret this result as indicating that individuals on Facebook have potentially tremendous reach. Shared content only needs to advance a few steps across Facebook’s social network to reach a substantial fraction of the world’s population.

We have found that the Facebook social network is nearly fully connected, has short average path lengths, and high clustering. Many other empirical networks, social and non-social, have also been observed with these characteristics, and Watts and Strogatz called networks with these properties ‘small world networks’"

Richard Elwes originally shared this post:

Online social networks such as, erm, Facebook have sparked the development of a new form of mathematical sociology. In this paper, for example, Frigyes Karinthy's old, essentially unprovable hunch that there should be 6 degrees of separation between most pairs of people on the planet receives solid supporting evidence:

"….fully 92% of all pairs of Facebook users were within five degrees of separation, and 99.6% were within six degrees. Considering the social network of only U.S. users, 96% were within five degrees and 99.7% were within six degrees."

[1111.4503] The Anatomy of the Facebook Social Graph

Abstract: We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and fri…