考虑加权传播率和随机干扰的谣言传播模型

A Rumor Propagation Model Considering Weighted Propagation Rate and Stochastic Noise

摘要: 在线社交网络已经成为互联网信息时代的信息传播的主要途径，对社交网络中谣言的性质、特征以及信息传播的研究一直是一项重要的研究课题。考虑社交网络环境及用户都会受到不确定因素的影响，网络结构和用户数量都会随时间发生变化，因此，在谣言传播过程中引入随机噪声；同时针对个体间的差异性，以及不同个体间连接紧密程度不同，引入加权传播率，基于此建立考虑加权传播率和随机干扰的谣言传播模型，并对此模型进行了传播动力学研究。推导了全局正解存在唯一性，推导了谣言消亡条件；并通过蒙特卡洛方法在BBV网络(加权无标度网络)以及LW网络(局域世界演化网络)上进行了仿真，验证了理论推导的合理性。实验结果表明，局域世界特性会加速谣言传播，扩大谣言最终规模；传播率的差异性能够抑制谣言峰值和最终规模；在保证网络拓扑结构不出现剧烈变化的情况下，弱噪声的加入会加速谣言的传播。

Abstract: Online social networks have become the primary channel for information dissemination in the Internet information age, making the study of the nature and characteristics of rumors in social networks, as well as the research on information propagation, an important subject of research. Considering that the social network environment and users are subject to the influence of uncertain factors, and that network structure and user numbers change over time, Stochastic noise is introduced into the rumor propagation process. At the same time, to account for the individual differences and the varying degrees of connection tightness between different individuals, a weighted transmission rate is introduced. Based on this, a rumor propagation model considering the weighted transmission rate and stochastic noise is established, and the dynamics of propagation for this model are studied. The uniqueness of the existence of the global positive solution is deduced, and the conditions for the demise of rumors are deduced. The Monte Carlo method is used to simulate the BBV network (weighted scale-free network) and LW network (local world evolution network), and the rationality of the theoretical derivation is verified. The experimental results show that the local world characteristics will accelerate the spread of rumors and expand the final scale of rumors. The difference in transmission rate can suppress the peak and final scale of rumors. In the case of ensuring that the network topology does not change drastically, the addition of weak noise will accelerate the spread of rumors.