The paper "Geographic Routing in Social Networks" by David Liben-Nowell et al. explores the concept of geographic routing in social networks, where messages are forwarded based on geographical proximity. The authors use a large social network, the LiveJournal community, to study the relationship between friendship and geography. They find that approximately 70% of friendships are influenced by geographical proximity, but existing models that predict friendship solely based on geographic distance are insufficient to explain these friendships. To address this, they propose a new model called rank-based friendship, which suggests that the probability of a friendship is inversely proportional to the number of closer people. This model is shown to explain the navigability of the social network, as it allows for the discovery of short paths to destination cities. The authors also prove analytically that under the rank-based friendship model, short chains can be discovered in any network with this relationship. The study highlights the importance of geography in social networks and provides a theoretical framework for understanding and improving routing algorithms in such networks.The paper "Geographic Routing in Social Networks" by David Liben-Nowell et al. explores the concept of geographic routing in social networks, where messages are forwarded based on geographical proximity. The authors use a large social network, the LiveJournal community, to study the relationship between friendship and geography. They find that approximately 70% of friendships are influenced by geographical proximity, but existing models that predict friendship solely based on geographic distance are insufficient to explain these friendships. To address this, they propose a new model called rank-based friendship, which suggests that the probability of a friendship is inversely proportional to the number of closer people. This model is shown to explain the navigability of the social network, as it allows for the discovery of short paths to destination cities. The authors also prove analytically that under the rank-based friendship model, short chains can be discovered in any network with this relationship. The study highlights the importance of geography in social networks and provides a theoretical framework for understanding and improving routing algorithms in such networks.