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Indicators

Meaning of this indicator
Similar to the previous case, it is conceivable that two scientists have
the same total number of citations, but that for one of them citations are
more or less evenly distributed over her career, while for the other cita-
tions are heavily concentrated (say, essentially for one top article). The
career years h-index by citations makes a distinction between such cases.
Also here the h-core of the career years h-index by citations is of impor-
tance. It brings together the years in which a scientist published their
most-cited articles.

Case 3: Citations and publication years: the career years h-index by
citations (a variant)
For each year we determine the sum of all citations received in that year.
Again, many variants are possible by restricting publications, similar to the
two previous cases. The years in this time series are arranged in descending
order of citations, leading to a new h-type list. The corresponding citation-
based h-index is then defined as the highest rank such that during the first h
years (in the list, not chronologically) at least h citations were received.
Before discussing other h-type indices we note that a year-based h-
index is not suited for cases where citations can easily be high such as
e.g., for countries, as the number of years under consideration is always
relatively small.

7.5 H-TYPE INDICES THAT TAKE THE NUMBER
OF RECEIVED CITATIONS BY HIGHLY CITED
PUBLICATIONS INTO ACCOUNT

7.5.1 The g-index
Perhaps the most famous variation on the h-index is the g-index, intro-
duced by Egghe (2006a,b,c). It is defined as follows: As for the calculation
of the h-index articles are ranked in decreasing order of received number
of citations. Then the g-index of this set of articles is defined as the
highest rank g such that the first g articles together received at least g 2
citations. This can be reformulated as follows: the g-index of a set of arti-
cles is the highest rank g such that the first g ( .0) articles have an average
number of citations equal to or higher than g. Indeed:
g g
X 2 1 X
c j $ g 3 c j $ g (7.10)
g
j51 j51