Abstract: The influence of intimacy between nodes in real social networks in the process of rumor spreading is considered. A new SI2R propagation model is proposed to establish rumor propagation dynamics equations to study the rumor propagation characteristics on scale-free networks. The non-consistence of rumor spreading rate among different nodes in this model depends on both node degree and intimacy degree, and the threshold expression of rumor propagation on scale-free network is obtained theoretically. Subsequently, the impact of node intimacy on the rumor propagation process in BA （Barabási-Albert） scale-free networks is simulated and the simulation results are validated using two real network datasets, Twitter and Live Journal. The result shows that the average intimacy of nodes in scale-free networks decreases with the increase of network clustering coefficient and as the average intimacy of nodes in networks increases, the final range of rumor propagation becomes larger. The study also finds that the existence of node intimacy makes the existence of propagation threshold in scale-free networks, and the propagation threshold decreases with the increase of the average intimacy of nodes.

Key words: rumor spreading, scale-free network, node intimacy function, propagation threshold, cluster coefficient

摘要： 考虑到真实社交网络中节点间亲密程度对谣言传播的影响，提出一种新的SI2R传播模型，建立谣言传播动力学方程组，研究谣言在无标度网络上的传播特性。该模型中不同节点间谣言传播率的非一致性同时取决于节点度与节点间亲密度，理论分析得到了无标度网络上谣言传播阈值表达式。随后，在BA（Barabási-Albert）无标度网络中就节点亲密度对谣言传播过程的影响进行了仿真实验，并利用Twitter和Live Journal两种真实网络数据集对仿真结果进行验证。研究表明，无标度网络中节点间平均亲密度随网络聚类系数的增大而减小，随着网络中节点间平均亲密度增大，谣言传播最终范围变大。研究还发现，节点间亲密度的存在使无标度网络中存在传播阈值，传播阈值随着节点间平均亲密度增大而减小。

关键词: 谣言传播, 无标度网络, 节点亲密度函数, 传播阈值, 聚类系数