Four degrees of separation

Abstract

Frigyes Karinthy, in his 1929 short story Lancszemek (in English, Chains) suggested that any two persons are distanced by at most six friendship links.1 Stanley Milgram in his famous experiments challenged people to route postcards to a fixed recipient by passing them only through direct acquaintances. Milgram found that the average number of intermediaries on the path of the postcards lay between 4:4 and 5:7, depending on the sample of people chosen. We report the results of the first world-scale social-network graph-distance computations, using the entire Facebook network of active users (≈ 721 million users, ≈ 69 billion friendship links). The average distance we observe is 4:74, corresponding to 3:74 intermediaries or degrees of separation, prompting the title of this paper. More generally, we study the distance distribution of Facebook and of some interesting geographic subgraphs, looking also at their evolution over time. The networks we are able to explore are almost two orders of magnitude larger than those analysed in the previous literature. We report detailed statistical metadata showing that our measurements (which rely on probabilistic algorithms) are very accurate.