Proof of six degrees of separation
Researchers from Microsoft analyzed 30 billion Microsoft Instant Messenger conversations, finding that average path length, or degree of separation, among the anonymized users probed was 6.6.
In a research paper from June 2007, titled "Worldwide Buzz: Planetary-Scale Views on an Instant-Messaging Network (PDF)," Eric Horvitz of Microsoft Research and Jure Leskovec of Carnegie Mellon University analyzed 30 billion conversations among 240 million people using Microsoft Instant Messenger in June 2006. It turned out that the average path length, or degree of separation, among the anonymized users probed was 6.6.
Six degrees of separation posits that a person is a step away from people they know and two steps distant from people known by the people they know--thus the magic number six.
We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We examine characteristics and patterns that emerge from the collective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset contains summary properties of 30 billion conversations among 240 million people. From the data, we construct a communication graph with 180 million nodes and 1.3 billion undirected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We investigate on a planetary-scale the oft-cited report that people are separated by "six degrees of separation" and find that the average path length among Messenger users is 6.6. We also find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender.
See also Nature, "Six Degrees of Messaging"