Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, P. R. China.
Sci Rep. 2019 Mar 25;9(1):5089. doi: 10.1038/s41598-019-41555-w.
The neighborhood network structure plays an important role in the collective opinion of an opinion dynamic system. Does it also affect the intervention performance? To answer this question, we apply three intervention methods on an opinion dynamic model, the weighted DeGroot model, to change the convergent opinion value [Formula: see text]. And we define a new network feature Ω, called 'network differential degree', to measure how node degrees couple with influential values in the network, i.e., large Ω indicates nodes with high degree is more likely to couple with large influential value. We investigate the relationship between the intervention performance and the network differential degree Ω in the following three intervention cases: (1) add one special agent (shill) to connect to one normal agent; (2) add one edge between two normal agents; (3) add a number of edges among agents. Through simulations we find significant correlation between the intervention performance, i.e., [Formula: see text] (the maximum value of the change of convergent opinion value [Formula: see text]) and Ω in all three cases: the intervention performance [Formula: see text] is higher when Ω is smaller. So Ω could be used to predict how difficult it is to intervene and change the convergent opinion value of the weighted DeGroot model. Meanwhile, a theorem of adding one edge and an algorithm for adding optimal edges are given.
邻里网络结构在意见动态系统的集体意见中起着重要作用。它是否也会影响干预效果？为了回答这个问题，我们在意见动态模型——加权 DeGroot 模型上应用了三种干预方法，以改变收敛意见值 [Formula: see text]。我们定义了一个新的网络特征 Ω，称为“网络差分度”，用于衡量节点度与网络中影响力值的耦合程度，即较大的 Ω 表示具有较高度数的节点更有可能与较大的影响力值耦合。我们在以下三种干预情况下研究了干预效果与网络差分度 Ω 之间的关系：（1）向一个正常代理添加一个特殊代理（水军）以进行连接；（2）在两个正常代理之间添加一条边；（3）在代理之间添加一些边。通过模拟，我们发现干预效果，即 [Formula: see text]（收敛意见值 [Formula: see text] 的最大变化值）与所有三种情况下的 Ω 之间存在显著相关性：当 Ω 较小时，干预效果 [Formula: see text] 更高。因此，Ω 可以用来预测干预和改变加权 DeGroot 模型的收敛意见值的难度。同时，给出了添加一条边的定理和添加最优边的算法。
