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_16: How information spreads through a social network? Can we assume, that the information is spread only through a given social network graph? What is the correct way to compare the models of information flow? These are the basic questions we address in this work. We focus on meticulous comparison of various, well-known models of rumor propagation in the social network. We introduce the model incorporating mass media and effects of absent nodes. In this model the information appears spontaneously in the graph. Using the most conservative metric, we showed that the distribution of cascades sizes generated by this model fits the real data much better than the previously considered models.
One of the greatest issue in analyzing the cascade size distribution is the lack of a good theoretical background for this process. Recently, researchers @cite_16 has presented new models, designed to fit real distribution of cascade sizes. Moreover, goodness of fit test against CGM model has been conducted. It turns out, that CGM works well for small cascades, however it is unreliable for the large ones. The introduction of time dependent parameters significantly improves predictions for the large cascades @cite_16 .