The Opinion Model And Its Analysis In A Social Network

Opinions exist in the social life everywhere. Almost all of us have our own opinions. Opinions can not only affect people’s words and actions, but also affect the management of the enterprise. Besides, opinions can help the related departments to make good decisions. In the Recent years, some people have put forward a lot of opinion models. According to the different opinion models, they did a lot of research and simulations. The paper provided a new opinion model combined with the existed models. From the point of the impact matrix, the paper explored the trend of the opinion formation in the whole group based on the different structures of the social networks.According to some conclusions of Markov chins in the condition of the time-invariant, the paper studied the trend of the opinions based on the impact matrix in two kinds of situations.One situation is that when the influence matrix is time-variant, the paper provided a special kind of neighbor model combined with the famous bounded confidence model and the opinion model provided in this paper. Based on this new model, the paper talked about the trend of the changes and the mechanisms of the opinion formation under the different structures of the social network. First of all. one simple case is that if the opinion in the social network has reached a consensus in the initial time, then no one will change their initial opinion. Second if people can not communicate with each other in the social network at some time, then people will keep their own opinion after that time. What’s more. if the structure is changing all the time, as long as the structure is fully connected at a certain moment, then the opinion in the whole network will reach a consensus at once. At last, if any two people in the group have the same neighbor, then people’s opinions in the social network will reach a consensus.Another situation is that the paper studied the problems of opinion consensus under different structures of social networks based on the opinion model provided in this paper. In this situation. the paper talked about whether people’s opinions can reach a consensus or not when the structure of social network is time-invariant. First of all, if the structure of the social network is time-invariant and the the transition probability matrices satisfy the condition of regularity in the initial time, then a consensus will be reached at last. Secondly, if the initiative group satisfies the above conditions and the structure of the passive group satisfies the following two conditions, then a consensus will be reached. One is that no one can communicate with each other in the passive group. And another is that the structure of the whole passive group is connected. According to the same situation, the paper extended the structure of the social network from the case of the time-invariant to the case of the time-variant. First, if every one in the social network has the same opinion at the beginning, then no one will change his opinion from the beginning to the last. Second, if every one has the same position in the social network in the process of changing their opinions, then a consessus will be reached at last. Finally, if the products of two neighbor matrices satisfy some conditions, then a consensus will also be reached at last.