The ability of a small set of coordinated actors to manipulate opinions in online social networks poses a serious challenge to the fairness and integrity of public debate. We investigate this problem by studying how targeted stubborn agents can shift the average opinion of a network governed by the Hegselmann-Krause bounded-confidence dynamics. Experiments are conducted on weighted LFR benchmark networks with community structure, using multiple node-selection strategies based on degree, strength, PageRank, betweenness, k-coreness, s-coreness, and salience. We compare static interventions, in which stubborn agents keep a fixed extreme opinion, with dynamic interventions, in which their opinion gradually evolves from moderate to extreme values. Results show that dynamic strategies are substantially more effective than static ones, as they exploit bounded-confidence dynamics to progressively recruit intermediate agents and extend influence across the network. In contrast, static strategies tend to create early opinion separation and therefore have a more limited reach. We also find that while some centrality measures offer advantages in static settings, dynamic interventions can achieve strong performance even with simple or random node selection. Overall, the study clarifies how intervention design and target selection interact in shaping collective opinions, with implications for understanding and countering manipulation in social networks.

翻译：一小部分协调行动者操控在线社交网络舆论的能力，对公共讨论的公平性和完整性构成了严重挑战。我们通过研究目标性顽固个体如何在Hegselmann-Krause有界置信动力学支配的网络中改变平均观点来探讨这一问题。实验在具有社区结构的加权LFR基准网络上进行，采用基于度、强度、PageRank、介数、k-核度、s-核度和显著性的多节点选择策略。我们比较了静态干预（顽固个体保持固定极端观点）与动态干预（其观点从温和值逐步演变为极端值）的效果。结果表明，动态策略比静态策略更加有效，因为它们利用有界置信动力学逐步吸纳中间个体，并将影响力扩展至整个网络。相比之下，静态策略容易造成早期观点分裂，因此影响范围较为有限。我们还发现，尽管某些中心性指标在静态设置中具有优势，但动态干预即使在简单或随机节点选择下也能取得强劲表现。总体而言，本研究阐明了干预设计与目标选择如何共同塑造群体观点，对理解并抵御社交网络中的操纵行为具有启示意义。