Generalizations of Egghe's g-index

Jorge Hirsch (2005) proposed the h-index (or Hirschindex) as a tool for quantifying the scientific productivity and the scientific impact of an individual researcher: “A scientist has index h if h of his or her n articles have at least h citations each, whereas the other n− h articles have at most h citations each.” The main strength (and perhaps the main weakness) of the Hirsch-index is that it is a robust, very simple, and fairly primitive indicator. It has attracted a lot of attention, and it has been applied to a variety of areas; see for instance Ball (2005), Cronin and Meho (2006), Glänzel (2006), Liu and Rousseau (2007), Oppenheim (2007), and van Raan (2006). Note that the h-index ignores the number of citations to each individual publication beyond what is needed to achieve a certain h-index. So what do we really know about a researcher with an h-index of 5? Perhaps this researcher is Professor X who has reached a meager total of 25 citations (5 papers with 5 citations). Or perhaps this researcher is the famous Mister Y whose research has attracted more than 1000 citations (5 papers with 200 citations plus another 50 papers each with 5 citations). Since the h-index fails to separate Professor X from Mister Y, Leo Egghe (2006a) proposed the so-called g-index, which assigns more weight to highly cited publications: “A scientist has index g if g is the largest