Scaling Properties Of Random Networks Under Proximity-Based Social Relations

We present an analytical framework to investigate the interplay between a communication graph and an overlay of social relationships. Particularly, we focus on geographical distance as the key element that interrelates the concept of routing in a communication network with interaction patterns on the social graph. Through this regime, we attempt to identify classes of social relationships that let the ensuing system scale, i.e., accommodate a large number of users given only finite amount of resources. We establish that stochastically localized communication patterns are indispensable to network scalability.