The threshold model as a classical paradigm for studying information spreading processes has been well studied. The main focuses are on how the underlying social network structure or the size of initial seeds can affect the cascading dynamics. However, the influence of node characteristics has been largely ignored. Here, inspired by empirical observations, we extend the threshold model by taking into account lurking nodes, who rarely interact with their neighbors. In particular, we consider two different scenarios: (i) Lurkers are absolutely silent and never interact with others and (ii) lurkers intermittently interact with their neighborhood with an activity rate $p$. In the first case, we demonstrate that lurkers may reduce the effective average degree of the underlying network, playing a dual role in spreading dynamics. In the latter case, we find that the stochastic dynamic behavior of lurkers could significantly promote the spread of information. Concretely, slightly raising the activity rate $p$ of lurkers may result in a remarkable increase in the final cascade size. Further increasing $p$ could make nodes become more stable on average, while it is still easy to observe global cascades due to the fluctuations of the effective degree of nodes.

中文翻译：

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潜伏者在阈值驱动的信息传播动态中的作用

阈值模型作为研究信息传播过程的经典范式已经得到很好的研究。主要关注点在于底层社交网络结构或初始种子的大小如何影响级联动态。然而，节点特性的影响在很大程度上被忽略了。在这里，受经验观察的启发，我们通过考虑很少与邻居交互的潜伏节点来扩展阈值模型。特别地，我们考虑了两种不同的情况：（i）潜伏者绝对沉默，从不与他人互动；（ii）潜伏者以活动率间歇性地与他们的邻居互动$磷$. 在第一种情况下，我们证明了潜伏者可能会降低底层网络的有效平均度，在传播动态方面发挥双重作用。在后一种情况下，我们发现潜伏者的随机动态行为可以显着促进信息的传播。具体来说，稍微提高活动率$磷$潜伏者的数量可能会导致最终级联大小的显着增加。进一步增加$磷$ 可以使节点平均变得更加稳定，同时由于节点有效度的波动仍然很容易观察到全局级联。