We study a rumor spreading model where individuals are connected via a network structure. Initially, only a small subset of the individuals are spreading a rumor. Each individual who is connected to a spreader, starts spreading the rumor with some probability as a function of their trust in the spreader, quantified by the Jaccard similarity index. Furthermore, the probability that a spreader diffuses the rumor decreases over time until they fully lose their interest and stop spreading. We focus on determining the graph parameters which govern the magnitude and pace that the rumor spreads in this model. We prove that for the rumor to spread to a sizable fraction of the individuals, the network needs to enjoy ``strong'' expansion properties and most nodes should be in ``well-connected'' communities. Both of these characteristics are, arguably, present in real-world social networks up to a certain degree, shedding light on the driving force behind the extremely fast spread of rumors in social networks. Furthermore, we formulate a large range of countermeasures to cease the spread of a rumor. We introduce four fundamental criteria which a countermeasure ideally should possess. We evaluate all the proposed countermeasures by conducting experiments on real-world social networks such as Facebook and Twitter. We conclude that our novel decentralized countermeasures (which are executed by the individuals) generally outperform the previously studied centralized ones (which need to be imposed by a third entity such as the government).

翻译：我们研究了一个谣言传播模型，其中个体通过网络结构相互连接。初始时，仅有一小部分个体在传播谣言。每个与传播者相连的个体，会以一定的概率开始传播谣言，该概率取决于他们对传播者的信任程度，并由杰卡德相似指数量化。此外，传播者扩散谣言的概率随时间递减，直至完全失去兴趣并停止传播。我们重点确定了在该模型中决定谣言传播规模与速度的图参数。我们证明，为使谣言传播至相当大比例的个体，网络需具备“强”扩展性质，且大多数节点应位于“高度连通”的社区中。这两大特征，可以说在一定程度上在现实社交网络中均存在，这揭示了谣言在社交网络中极速传播背后的驱动力。此外，我们提出了一系列广泛的应对措施以遏制谣言传播。我们引入了四项理想应对措施应具备的基本标准。通过在Facebook和Twitter等现实社交网络上进行实验，我们评估了所有提出的应对措施。结论表明，我们提出的新型去中心化应对措施（由个体执行）通常优于先前研究的中心化措施（需由第三方实体如政府强制执行）。