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 [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.
@cite_8: graph involving over 31,000 individuals. We found that information spreading displays a non-Markovian branching dynamics that can be modeled by a twostep Bellman-Harris Branching Process that generalizes the static models known in the literature and incorporates the high variability of human behavior. It explains accurately all the features of information propagation under the -point" and can be used for prediction and management of viral information spreading processes.
Iribarren moro have developed the similar model, where an integro-differential equations have been introduced. That equations describe the cascade sizes when the number of messages send by a node is described by the Harris discrete distribution.However, the general solution to their equations is not known and merely solutions for nontrivial cases (e.g., superexponential processes @cite_8 ) has been considered. Our discoveries provide much simpler method and lucidly explain, that the underlying social graph is far more complex than just the graph of followers.