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不和、破坏民主和动摇社区稳定的攻击者的目标。其目标往往不是支持冲突中的某一方，而是增加分歧和极化。为了从数学角度理解此类攻击，研究者运用社会学中的意见形成模型（如Friedkin-Johnsen模型），并形式化研究当攻击者仅改变少数用户的意见时，其能造成的最大不和程度。此类研究中通常假设攻击者完全掌握网络拓扑结构及所有用户的意见。然而，后者在实际中往往不切实际，因为用户意见通常不可获取或难以精确估计。为解决这一问题，我们提出以下疑问：即使攻击者仅知晓网络拓扑结构，是否仍能在社交网络中播下不和的种子？我们对此给出肯定回答。本文提出近似算法，用于检测网络中与分歧和极化高度相关的小规模用户集合。研究表明，当攻击者激化这些用户，且网络初始分歧/极化程度不高时，我们的方法在已知用户意见的场景下可实现常数因子近似。为寻找具有影响力的用户集合，我们针对带正负边权的图上的MaxCut变体问题，提出了一种新型近似算法。通过仅依赖网络拓扑结构的实验评估，我们发现该方法在性能上与同时掌握网络拓扑及所有用户意见的方法相当。此外，我们给出了NP难性证明，该问题曾是Chen与Racz提出的开放性问题[IEEE Trans. Netw. Sci. Eng., 2021]。