The Opinion Model And Analysis In Social Network Based On Gossip Algorithm

Gossip exists in the social life everywhere. With the development and improvement of communication technology, the spread of rumors will be faster and the impact on the society at the same time also will be greater. So the problem of opinion consensus under the impact of rumors attracts the attention of many scholars. In the resent years, people has done in-depth research and applied the gossip algorithm to other networks. In this paper, we make a new opinion model based on gossip algorithm and combine with more character in society. From the perspective of network topology, collective opinion formation and evolution are discussed.According to the characteristics of the Gossip algorithm, this paper studies the trend of the opinions and the influence factors in two parties.In the first part, we provide a new gossip algorithm to investigate the problem of opinion consensus with the time-varying influence factors and weakly connected graph among multiple agents. What is more, we discuss not only the effect of the time-varying factors and the randomized topological structure but also the spread of misinformation and communication constrains described by probabilistic quantized communication in the social network. Under the underlying weakly connected graph, we first denote that all opinion states converge to a stochastic consensus almost surely; that is, our algorithm indeed achieves the consensus with probability one. Furthermore, our results show that the mean of all the opinion states converges to the average of the initial states when time-varying influence factors satisfy some conditions. Finally we give a result about the square mean error between the dynamic opinion states and the benchmark without quantized communication.In the second part, we provide a model to investigate the tension containing information aggregation, communication limit, prejudices and trust selection. In the social network, we characterize how the presence of trust selection interferes with communication limit expressed by probabilistic quantized communication and prejudices mean by the initial belief. We show that, although the resulting dynamics persistently oscillates, its average is a stable opinion profile, which is not a consensus in the strongly connected structure. This means that the expected beliefs of an agent will not in general achieve, even asymptotically, an agreement with the other agents in the society. But the average beliefs of an agent will converge to this stable state in square mean error. Meanwhile, we prove that the opinion consensus will be reached without considering the prejudice and the stable state will be no relevant to the probability of trust selection if the influence matrix is symmetric. Finally we conduct the algorithm with the time-varying probability and get the conditions for time-varying probability to achieve consistency for further research on trust with each other and without considering the communication constraints.