Liben-Nowell, David; Novak, Jasmine; Kumar, Ravi; Raghavan, Prabhakar; Tomkins, Andrew

Proceedings of the National Academy of Sciences of the United States of America (2005), 102(33), 11623-11628 CODEN: PNASA6; ISSN: 0027-8424. English.

We live in a "small world," where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Exptl. studies have verified this property in real social networks, and theor. models have been advanced to explain it. However, existing theor. models have not been shown to capture behavior in real-world social networks. Here, we introduce a richer model relating geog. and social-network friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one-third of the friendships are independent of geog. and the remainder exhibit the proposed relationship. Further, we prove anal. that short chains can be discovered in every network exhibiting the relationship.