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作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，防御联盟是一种量化群体结构形式。然而，现有关于联盟的研究均忽略了一个对联盟形成具有直观核心意义的方面——假设智能体对其他智能体的态度存在先验倾向：它们倾向于与其喜欢的智能体共同组成群体（联盟），从而乐于互助以实现共同目标，并可能共同对抗其厌恶的群体外智能体。心理学文献中引入的符号网络通过自然推广图结构，对智能体间的喜恶关系进行建模。因此，我们提出符号网络中防御联盟的新概念，并研究与此概念相关的若干基础算法问题。这些算法问题与组合学发现共同将我们的概念与相关性聚类（符号网络中一种成熟的智能体群体识别方法）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，并展示一种可在符号图中找到最小防御联盟的参数化算法。