The model identifies the boundary of the global cascade regime in each case. Concretely, it is observed that the simulations can easily pass the regime boundary for both the original threshold model and the lurker model due to low activity rate p or large threshold.
The overall picture is consistent with the numerical results of models in refs. (23,25). The probability of observing global cascades is strongly influenced by the activity rate of lurkers. The emergence of global cascades depends on both the activity rate p and threshold.
Further, we demonstrate that the statistics of cascades display an interesting difference between the original threshold model and the lurker model. Particularly, the probability distribution of cascade sizes exhibits a power-law-like behavior in both models. Nevertheless, the distribution exhibits a plateau in the lurker model, which is absent in the original model. The presence of the plateau is due to the fluctuation of the effective degree of lurkers, which makes nodes with small degrees more vulnerable to attack from global cascades.
Frequency Fg of global cascades as a function of node threshold and activity rate p for different values of f: (a) f=0, corresponding to the original threshold model, and (b) f=0.5. The red lines show the boundary of the global cascade regime according to Eq. (7). Simulations correspond to an ER network with size N=5000 and are averaged over 104 realizations.
In summary, we have investigated two different models of spreading processes to understand how the underlying network affects the dynamics of information spreading. Our findings suggest that the introduction of lurkers may significantly enhance the spreading efficiency of information.
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One of the drawbacks to this approach was that we needed to recompile every time we made even a small change to the code. This slowed everything else we were doing down and because we couldn't always have someone waiting for the application to finish building. 827ec27edc