【摘要】 本文将超图结构、概率行为与信息理论三者进行合理综合,并将它们应用到在线社交网络及其隐性影响力评估的研究中,从而提出了一种新的有效数学分析方法.本文首先利用超图理论并通过超路径建立了在线社交网络中用户之间的信息传播过程,同时结合概率行为描述了信息传播的量化关系与波动强度.然后,本文通过平均互信息提出了一种新的在线社交网络隐性影响力评估的量化方法,同时也使用数值算例验证了这种评估方法的有效性.更多还原

【Abstract】 This paper sets up a reasonable synthesis among hypergraph structure, probability behavior and information theory, and applies them to the study of online social networks. This motivates us in this paper to provide a new mathematical method for analyzing online social networks and their hidden influence. Therefore,this paper first applies hypergraph theory to set up the information transmission process by means of a hyperpath between any two users, and describes quantitative relation and fluctuation strength through combining hypergraph structure with probabilistic behavior. Then the average mutual information is established to provide a new mathematical evaluation method of hidden influence. Numerical examples verify the effectiveness of the evaluation method of hidden influence.更多还原