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The log-log plot of the cascade size distribution on the Twitter dataset. It follows a powerlaw with an exponent −2.3.
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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...
Contexts in source publication
Context 1
... the simulation registered an obvious phase transition (the cas- cades are either extremely large or are smaller than 100) (see Figure 2). No such gap has been observed in the real data (see Figure 1). Second, the probability of the large cascade is intolerably high in simulations. ...
Context 2
... et al. [18] suggest that the information propagation in the network of recom- mendations may produce cascades with desired exponent. However, in the real data, the parameter γ can be com- pletely different (e.g., see Figure 1 of the Twitter cascade size distribution with power-law exponent γ = −2.3). To adopt our rdag(n, p) model to those cases, one can customize a distribution of random cascades (we assumed a fairly sim- ple method to generate them). ...
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