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. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in real-world social networks. Here we introduce a richer model relating geography 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 geography, and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in every network exhibiting the relationship.
In REF , experimental results based on the LiveJournal social network 3 demonstrated a close relationship between geographic distance and probability distribution of friendship, where the probability of befriending a particular user on LiveJournal is inversely proportional to the positive power of the number of closer users.
Geographic Routing in Social Networks ∗
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine