The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex sets from graph theory. This geometric approach allows for a beautiful characterization of these sets. The application of geometry is not limited to the description of contextuality sets alone; it also plays a crucial role in defining contextuality quantifiers based on geometric distances. These quantifiers are particularly significant in the context of the resource theory of contextuality, which emerged following the recognition of contextuality as a valuable resource for quantum computation. In this paper, we provide a comprehensive review of the geometric aspects of contextuality. Additionally, we use this geometry to define several quantifiers, offering the advantage of applicability to other approaches to contextuality where previously defined quantifiers may not be suitable. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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关于语境图方法的几何方面

情境性和图论之间的联系为该领域的众多进步铺平了道路。一个值得注意的发展是认识到许多上下文场景中的概率分布集可以使用图论中完善的凸集来有效地描述。这种几何方法可以对这些集合进行美丽的表征。几何学的应用不仅仅局限于上下文集合的描述；它还在定义基于几何距离的上下文量词方面发挥着至关重要的作用。这些量词在上下文资源理论的背景下特别重要，该理论是在认识到上下文作为量子计算的宝贵资源之后出现的。在本文中，我们对语境性的几何方面进行了全面的回顾。此外，我们使用这种几何形状来定义几个量词，从而提供了适用于其他上下文方法的优势，而先前定义的量词可能不适合。本文是“量子背景、因果关系和选择自由”主题的一部分。