Defensive Alliances in Signed Networks
Emmanuel Arrighi, Zhidan Feng, Henning Fernau, Kevin Mann, Xingqin Qi,, Petra Wolf

TL;DR
This paper introduces the concept of defensive alliances in signed networks, analyzing their properties and proposing algorithms to find minimal alliances, thereby extending community detection methods to include liking and disliking relationships.
Contribution
It proposes a novel notion of defensive alliances in signed networks and develops parameterized algorithms to identify minimal alliances, connecting to correlation clustering.
Findings
Defined defensive alliances in signed networks.
Connected alliances to correlation clustering.
Developed a parameterized algorithm for finding smallest alliances.
Abstract
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…
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Taxonomy
TopicsComplex Network Analysis Techniques · Opinion Dynamics and Social Influence · Evolutionary Game Theory and Cooperation
