The Scaling laws of Spatial Structure in Social Networks

Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social networks have been studied extensively. Many important universal properties with which we are quite familiar have been recovered, such as scale free degree distribution, small world, community structure, self-similarity and navigability. According to some empirical investigations, we conclude that our social network also possesses another important universal property. The spatial structure of social network is scale invariable. The distribution of geographic distance between friendship is about $Pr(d)\propto d^{-1}$ which is harmonious with navigability. More importantly, from the perspective of searching information, this kind of property can benefit individuals most.