The analysis of (social) networks and multi-agent systems is a central theme in Artificial Intelligence. Some line of research deals with finding groups of agents that could work together to achieve a certain goal. To this end, different notions of so-called clusters or communities have been introduced in the literature of graphs and networks. Among these, defensive alliance is a kind of quantitative group structure. However, all studies on the alliance so for have ignored one aspect that is central to the formation of alliances on a very intuitive level, assuming that the agents are preconditioned concerning their attitude towards other agents: they prefer to be in some group (alliance) together with the agents they like, so that they are happy to help each other towards their common aim, possibly then working against the agents outside of their group that they dislike. Signed networks were introduced in the psychology literature to model liking and disliking between agents, generalizing graphs in a natural way. Hence, we propose the novel notion of a defensive alliance in the context of signed networks. We then investigate several natural algorithmic questions related to this notion. These, and also combinatorial findings, connect our notion to that of correlation clustering, which is a well-established idea of finding groups of agents within a signed network. Also, we introduce a new structural parameter for signed graphs, signed neighborhood diversity snd, and exhibit a parameterized algorithm that finds a smallest defensive alliance in a signed graph.

翻译：（社会）网络与多智能体系统的分析是人工智能领域的核心主题。部分研究关注寻找能够协同实现特定目标的智能体群体。为此，图与网络文献中引入了多种所谓的聚类或社群概念。其中，防御联盟是一种定量群体结构。然而，迄今为止关于联盟的所有研究都忽略了一个对联盟形成具有直观基础的核心方面——即假定智能体对其他智能体的态度存在先决条件：它们倾向于与自身喜欢的智能体组成群体（联盟），从而乐于为共同目标相互协助，并有可能共同对抗其不喜欢的群体外智能体。心理学文献中引入的符号网络通过自然推广图论模型，刻画了智能体间的喜好与厌恶关系。据此，我们提出符号网络背景下防御联盟的新概念。随后，我们研究了与该概念相关的若干自然算法问题。这些算法问题及组合发现将我们的概念与相关聚类（一种在符号网络中寻找智能体群体的成熟思想）联系起来。此外，我们引入符号图的新结构参数——符号邻域多样性（snd），并提出一种参数化算法，用于在符号图中寻找最小防御联盟。