标题： 具有顽固个体的影响网络中社会权力的分布式感知 显示英文标题

标题： Distributed perception of social power in influence networks with stubborn individuals

摘要： 社会权力量化了个体影响他人的能力，在社会影响力网络中起着核心作用。然而，计算社会权力通常需要全局知识以及显著的计算或存储能力，特别是在具有顽固个体的大规模网络中。 本文开发了针对具有顽固个体群体的社会权力感知的分布式算法。我们基于Friedkin-Johnsen（FJ）意见动力学提出了两种用于社会权力分布式感知的动力学模型：一种没有反射评估，另一种有反射评估。在这两种情况下，我们的感知机制都从独立的初始感知开始，并主要依赖于局部信息：每个个体只需要知道其邻居的顽固性或自我评价、他们赋予的影响权重和群体规模即可。 我们提供了严格的动态系统分析以表征平衡点、不变集和收敛性的性质。确定了个体感知的社会权力收敛到实际社会权力的条件。所提出的感知机制对反射评估、非理性感知和时间尺度变化表现出很强的鲁棒性。 提供数值例子来说明我们的结果。 显示英文摘要

摘要： Social power quantifies the ability of individuals to influence others and plays a central role in social influence networks. Yet computing social power typically requires global knowledge and significant computational or storage capability, especially in large-scale networks with stubborn individuals. This paper develops distributed algorithms for social power perception in groups with stubborn individuals. We propose two dynamical models for distributed perception of social power based on the Friedkin-Johnsen (FJ) opinion dynamics: one without and one with reflected appraisals. In both scenarios, our perception mechanism begins with independent initial perceptions and relies primarily on local information: each individual only needs to know its neighbors' stubbornness or self-appraisals, the influence weights they accord and the group size. We provide rigorous dynamical system analysis to characterize the properties of equilibria, invariant sets and convergence. Conditions under which individuals' perceived social power converges to the actual social power are established. The proposed perception mechanism demonstrates strong robustness to reflected appraisals, irrational perceptions, and timescale variations. Numerical examples are provided to illustrate our results.