1 A theoretical discussion of Prathap’s h 2 -index for institutional evaluation with an application in the field of HIV infection and therapy Ronald Rousseau 1, 2 , Liying Yang 3 , Ting Yue 3 , 1 KHBO (Association K.U.Leuven), Industrial Sciences and Technology, Zeedijk 101, B-8400 Oostende, Belgium; ronald.rousseau@khbo.be 2 K.U.Leuven, Department of Mathematics, Celestijnenlaan 200B, 3001 Leuven (Heverlee), Belgium 3 National Science Library of the Chinese Academy of Science 33 Beisihuan Xilu, Zhongguancun, Beijing 100080, P.R.China yangly@mail.las.ac.cn , yuet@mail.las.ac.cn Abstract Hirsch-type indices are not only used for the evaluation of individual scientists but also for institutional evaluation. In particular, Prathap’s suggestion, using the pair of h-indices (h 1 -h 2 ) seems a promising approach. This paper discusses these h-indices, incorporating moreover a Molinari correction for size. We provide a theoretical framework and provide practical examples in the field of HIV infection and therapy. It is shown that the National Cancer Institute (NCI, USA) and Harvard University are the leading institutes in this field (in the world). If, however, size is controlled according to the Molinari approach, the National Institute of Allergy and Infectious Diseases (NIAID, USA) becomes the leader. In addition, we provide a new structural index: the ratio h 2 / h 1 . It is suggested that this ratio indicator is related to the stability of the research performed at an institute or university. The term stability is used here in the sense of not depending on a small group of scientists that could easily move to another university. Introduction Research evaluation of scientific institutes (universities, departments, independent research institutes) is one of the focal points in scientometric studies. The number of published articles and the number of citations received by these articles usually form the starting point of such evaluations. The h-index, introduced by Hirsch (2005), provides an interesting way of combining these two basic indicators. Let us recall that an institute has h-index h 1 (in a given timeframe) if h 1 is the largest natural number such that h 1 of the institute’s articles have received at least h 1 citations. This index has a number of practical advantages: it is not necessary to know the exact number of publications; once it is known that an article belongs to the h-core, or does certainly not belong to it, one must not determine the exact number of citations, and it avoids undue focus on the number of publications alone. Following Prathap (2006) we have denoted an institution’s h-index by h 1 . Of course, the h-index, like any other single number indicator, has also a number of drawbacks. For a review of advantages and disadvantages of the h-index in general we refer the reader to (Egghe, 2009;