Six Degrees of Separation in Online Society

Six degrees of separation is a well-known idea that any two people on this planet can be connected via an average number of six steps. Having succeeded in the real world, the theory even directly or indirectly motivated the invention of online societies. However, no much effort has been paid on checking if the theory really holds for online societies whose connection pattern may not be identical to the real world. This paper tries to give an answer to the question by both mathematical modeling and online measurements. The mathematical approach formulates the problem as a Minimum Diameter Problem in graph theory and evaluates the maximum and average values of the number of connections between any two random-selected community members. Measurements are conducted in three different kinds of online societies, namely ArnetMiner for academic researchers, Facebook for students, and Tencent QQ for teenagers in China. Analysis of these measurements verifies our theoretical findings. KeywordsSix degrees of separation, social network, minimum diameter problem, small world