Page 216 - Becoming Metric Wise

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Indicators

0
Here x ðjÞ 0 denotes the number of times authors i and i are coauthors
i;i
in a paper with j authors in total. The number q is the largest natural
number j such that f j 6¼ 0, and the number k is equal to the number of
elements in the set K 5 {j;j $ 2, f j 6¼ 0}.
The theory proposed by Egghe and English is the most refined
approach known for the moment. Yet even within this approach open
problems still exist, see the summary in (Egghe, 1991).

7.3 THE H-INDEX
7.3.1 Definition

Let us first recall the definition of the h-index as introduced by Hirsch
(2005). Consider the list of articles (co-)authored by scientist S, ranked
according to the number of citations each of these articles has received.
Articles with the same number of citations are given different rankings (for
the moment the exact order does not matter). Then the h-index of scientist
Sis h if the first h articles received each at least h citations, while the article
ranked h 1 1 received strictly less than h 1 1 citations. Stated otherwise,
0
scientist S h-index is h if h is the largest natural number (representing a
rank) such that the first h publications received each at least h citations.
The first h articles in such a ranked list form the h-core (Rousseau,
2006c). In case the articles themselves in the h-core are of importance in
the study and the source at rank h 1 1 has the same number of items
as the source at rank h, then there are two options. The first is to restrict
the h-core to exactly h elements. For this to happen one needs a second
(or even tertiary) criterion to rank sources. We suggest using age as the
secondary criterion and rank articles with the same number of citations in
antichronological order i.e., the most recent article first. Indeed such arti-
cles have a higher number of citations per year than others with the same
number of citations. A second option is to simply include all sources with
the same number of items as the source on rank h. In that case an h-core
can have any number of sources (but at least h). The resulting set is some-
times referred to as an extended h-core. Articles that do not belong to
the h-core are said to belong to the h-tail. It is further noted that if the
last article in the list occupies rank r and receives c . r citations then this
scientist’s h-index is equal to r.
Consider, for example, Table 7.2 of publications and citations, ranked
according to the number of received citations.