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order, h 1 is the standard h-index. Then the first h 5 h 1 numbers are
removed and one determines the h-index of the remaining n 2 h 1 items,
leading to h 2 . This process is continued until h k 5 0 or there are no more
items in the remaining sequence. For our example (100, 50, 20, 4, 2, 2,
1, 1, 0, .. ., 0) we find: h 5 h 1 5 4. The remaining sequence is (2, 2, 1, 1,
0, .. ., 0). Hence h 2 5 2. This leaves the sequence (1, 1, 0, .. ., 0). Hence
h 3 5 1 and also h 4 5 1; finally the procedure stops with h 5 5 0. For the
sequence (100, 50, 20, 4, 2) we find h 5 h 1 5 4; h 2 5 1 and the procedure
stops because there are no more items in the sequence. Such a sequence of
h-indices can be seen as a discrete characterization of a citation distribution.

7.16 CONCLUDING REMARKS

We end this chapter on indicators by referring the reader to a review of
the literature on citation impact indicators by Waltman (2016). It provides
an overview on bibliographic databases (WoS, Scopus, and GS) and fur-
ther covers the selection of publications and citations to be included in
the calculation of citation impact indicators, normalization issues related
to citation impact indicators, counting methods and journal citation
impact indicators. We especially draw attention to the four recommenda-
tions formulated in Waltman (2016).
• Do not introduce new citation impact indicators unless they have a
clear added value relative to existing indicators.
• Pay more attention to the theoretical foundation of citation impact
indicators.
• Pay more attention to the way in which citation impact indicators are
being used in practice.
• Exploit new data sources to obtain more sophisticated measurements
of citation impact.
Next we draw the readers’ attention to the interesting opinion paper
by Gla ¨nzel and Moed (2013), which discusses the following points:
A deterministic versus a probabilistic approach to indicators, application
related properties, time dependence of indicators, normalization issues,
size dependence and the use of network indicators. Ding and Cronin
(2011) point out the difference between popularity and prestige for
authors, but the difference can also be made for journals. Although both
can be considered to be measure of esteem, they are not the same. In
their investigation they operationalize the notion of popularity as the
number of times an author is cited and prestige as the number of times an