UC Santa Cruz

We present an analytical framework to investigate the interplay between a communication graph and an overlay of social  relationships.  We focus on geographical distance as the key element that interrelates the concept of routing in a communication network with the dynamics of interpersonal relations on the corresponding social graph. We 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 geographically concentrated communication patterns are indispensable to network scalability. We  further examine the impact of such proximity-driven interaction patterns on the throughput scaling of wireless networks, and show that, when social communications are geographically localized, the maximum per-node throughput scales approximately as $1/\log n$, which is significantly better than the well-known bound of $1/\sqrt{n \log n}$ for the uniform communication model.