Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain opinion and have a major effect on the collective opinion formation process. Based on a modified version of the network Laplacian we derive quantities capturing the transient dynamics of the system and the emerging stationary opinion states. In the case of a single stubborn agent we characterize his/her ability to coherently change a prevailing consensus. For two antagonistic stubborn agents we investigate the opinion heterogeneity of the emerging non-consensus states and describe their statistical properties using a graph metric similar to the resistance distance in electrical networks. Applying the model to synthetic and empirical networks we find while opinion diversity is decreased by small-worldness and favored in the case of a pronounced community structure the opposite is true for the coherence of opinions during a consensus change.

在一个简单的社会影响力模型泰勒模型的框架内，我们分析性地研究了顽固的主体在网络系统总体舆论动态中的作用。与狂热者相似，顽固的特工倾向于某种意见，并且对集体意见形成过程产生重大影响。基于网络拉普拉斯算子的修改版本，我们得出捕获系统瞬态动态和新兴的稳定观点状态的数量。对于一个single强的特工，我们描述了他/她连贯地改变一个普遍共识的能力。对于两种拮抗的顽固剂，我们研究了新兴的非共识状态的观点异质性，并使用类似于电网电阻距离的图形度量来描述其统计特性。