Bipolarization is a phenomenon in which either a large or very small information cascade appears randomly when the retweet rate is high. This phenomenon, which has been observed only in simulations, has the potential to significantly advance the prediction of final cascade sizes because forecasters need only focus on the two peaks in the final cascade size distribution rather than considering the effects of various details, such as network structure and user behavioral patterns. The phenomenon also suggests the difficulty of identifying factors that lead to the emergence of large-scale cascades. To verify the existence of bipolarization, this paper theoretically derives mathematical expressions of the cascade final size distribution using urn models, which simplify the diffusion behavior of actual online social networks. Under the assumption of infinite network size, the distribution exhibits power-law behavior, consistent with the results of existing diffusion models and previous Twitter analytical outcomes. Under the assumption of finite network size, bipolarization is observed.

双极化是一种现象，当转发率很高时，会随机出现大或非常小的信息级联。这种仅在模拟中观察到的现象有可能显着推进最终级联大小的预测，因为预测者只需要关注最终级联大小分布中的两个峰值，而不是考虑各种细节的影响，例如网络结构和用户行为模式。这种现象还表明很难确定导致大规模级联出现的因素。为了验证双极化的存在，本文使用瓮模型从理论上推导了级联最终大小分布的数学表达式，简化了实际在线社交网络的扩散行为。在无限网络规模的假设下，分布表现出幂律行为，与现有扩散模型的结果和之前的 Twitter 分析结果一致。在有限网络规模的假设下，观察到两极化。