Explicit agreement extremes for a $2\times2$ table with given marginals

Given two different clusterings of a data set, many measures ha ve been proposed to quantify their degree of concordance. A recent review of a representa tive number of them can be found in Meil a (2016). These measures are usually categori zed into three classes: those based on inspecting the assignments of data pairs in both clu sterings, those involving some cluster matching between the two clusterings, and those rel ying on information theoretic criteria. This paper concerns the first one of these classes. In fact, some of the most popular and widely used similarity measures, such as the Rand ind ex, the Jaccard index, or the Fowlkes-Mallows index, belong to this class of pair-based s imilarities, but it should be noted that there is a plethora of them, as explored in Albatineh, Niewiadomska-Bugaj and Mihalko (2006), Warrens (2008) or Warrens and van der Hoef (2019).