Theoretical Analysis of Geographic Routing in Social Networks

Abstract

We introduce a formal model for geographic social networks, and introduce the notion of rank-based friendship, in which the probability that a person v is a friend of a person u is inversely proportional to the number of people w who live closer to u than v does. We then prove our main theorem, showing that rank-based friendship is a sufficient explanation of the navigability of any geographic social network that adheres to it.