The Generation Mechanism of Degree Distribution with Power Exponent >2 and the Growth of Edges in Temporal Social Networks

The structures of social networks with power laws have been widely investigated. People have a great interest in the scale-invariant generating mechanism. We address this problem by introducing a simple model, i.e., a heuristic probabilistic explanation for the occurrence of a power law. In particular, the proposed model can be used to explain the generative mechanism that leads to the scale-invariant of the degree distribution with a power exponent of τ > 2 . Furthermore, a stochastic model (the pure birth points process) is used to describe the cumulative growth trend of edges of a temporal social network. We applied our model to online temporal social networks and found that both the degree distribution scaling behaviors and the growth law of edges can be quantitatively reproduced. We gained further insight into the evolution nature of scale-invariant temporal social networks from the empirical observation that the power exponent τ gradually decreases and approaches 2 or less than 2 over evolutionary time.