Statistical Behavior of Embeddedness and Communities of Overlapping Cliques in Online Social Networks

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, the authors provide empirical evidence on the existence of rich higher-order structural characteristics in online social networks, develop mathematical models to interpret and model these characteristics, and discuss their various applications in practice.