An exponential triangle model for the Facebook network based on big data

Social networks have become one of the most important research platforms in the big data era. Modelling social networks enables researchers and engineers to understand and analyze their intrinsic properties thereby implementing their real applications. A number of studies on social network modelling focus on a few characteristics, such as the number of edges (i.e., two-star motifs), scale-free degree distribution, and assortative property. This paper proposes an exponential triangle model for a typical social network, namely the Facebook network, established based on big data, and further analyzes its primary attributes of common interest on topological features. This new model has a power-law node-degree distribution with a flat top and an exponential cut-off tail, in remarkable agreement with one large-scale Facebook dataset. It can be used to predict future links of the Facebook network and help improve the friend-recommendation system. Furthermore, this work provides a useful graph-theoretic tool for Facebook network studies and enhances potential applications of social networks in general.