  We introduce random directed acyclic graph and use it to model the
information diffusion network. Subsequently, we analyze the cascade generation
model (CGM) introduced by Leskovec et al. [19]. Until now only empirical
studies of this model were done. In this paper, we present the first
theoretical proof that the sizes of cascades generated by the CGM follow the
power-law distribution, which is consistent with multiple empirical analysis of
the large social networks. We compared the assumptions of our model with the
Twitter social network and tested the goodness of approximation.
