  The Leiden Rankings can be used for grouping research universities by
considering universities which are not statistically significantly different as
homogeneous sets. The groups and intergroup relations can be analyzed and
visualized using tools from network analysis. Using the so-called "excellence
indicator" PPtop-10%--the proportion of the top-10% most-highly-cited papers
assigned to a university--we pursue a classification using (i) overlapping
stability intervals, (ii) statistical-significance tests, and (iii) effect
sizes of differences among 902 universities in 54 countries; we focus on the
UK, Germany, Brazil, and the USA as national examples. Although the groupings
remain largely the same using different statistical significance levels or
overlapping stability intervals, these classifications are uncorrelated with
those based on effect sizes. Effect sizes for the differences between
universities are small (w <.2). The more detailed analysis of universities at
the country level suggests that distinctions beyond three or perhaps four
groups of universities (high, middle, low) may not be meaningful. Given similar
institutional incentives, isomorphism within each eco-system of universities
should not be underestimated. Our results suggest that networks based on
overlapping stability intervals can provide a first impression of the relevant
groupings among universities. However, the clusters are not well-defined
divisions between groups of universities.
