In recent years, online social networks have been the target of adversaries who seek to introduce discord into societies, to undermine democracies and to destabilize communities. Often the goal is not to favor a certain side of a conflict but to increase disagreement and polarization. To get a mathematical understanding of such attacks, researchers use opinion-formation models from sociology, such as the Friedkin--Johnsen model, and formally study how much discord the adversary can produce when altering the opinions for only a small set of users. In this line of work, it is commonly assumed that the adversary has full knowledge about the network topology and the opinions of all users. However, the latter assumption is often unrealistic in practice, where user opinions are not available or simply difficult to estimate accurately. To address this concern, we raise the following question: Can an attacker sow discord in a social network, even when only the network topology is known? We answer this question affirmatively. We present approximation algorithms for detecting a small set of users who are highly influential for the disagreement and polarization in the network. We show that when the adversary radicalizes these users and if the initial disagreement/polarization in the network is not very high, then our method gives a constant-factor approximation on the setting when the user opinions are known. To find the set of influential users, we provide a novel approximation algorithm for a variant of MaxCut in graphs with positive and negative edge weights. We experimentally evaluate our methods, which have access only to the network topology, and we find that they have similar performance as methods that have access to the network topology and all user opinions. We further present an NP-hardness proof, which was an open question by Chen and Racz [IEEE Trans. Netw. Sci. Eng., 2021].

翻译：近年来，在线社交网络已成为试图在社会中制造分裂、破坏民主和动摇社区稳定的攻击者的目标。其目标往往不是偏向冲突的某一方，而是加剧分歧与极化。为从数学角度理解此类攻击，研究者采用社会学中的意见形成模型（如Friedkin--Johnsen模型），并正式研究当攻击者仅改变少量用户的意见时所能产生的分歧程度。在此类研究中，通常假设攻击者完全了解网络拓扑结构及所有用户的意见。然而，这一假设在实践中往往不切实际，因为用户意见可能无法获取，或难以准确估计。为解决此问题，我们提出以下疑问：即便仅知晓网络拓扑结构，攻击者能否在社交网络中播下分裂的种子？我们对此给出肯定回答。我们提出近似算法，用于检测网络中少数对分歧与极化具有高度影响力的用户。研究表明，当攻击者激进化这些用户，且网络初始分歧/极化程度不高时，我们的方法可达到与已知用户意见场景下常数因子近似相当的性能。为找到这些关键用户，我们针对带有正负边权重的图上的MaxCut变体问题，提出了一种新型近似算法。实验评估表明，仅依赖网络拓扑信息的方法，其性能与同时利用网络拓扑及所有用户意见的方法相近。此外，我们给出了问题的NP-hard性质证明，该问题曾由Chen与Racz公开提出[IEEE Trans. Netw. Sci. Eng., 2021]。