Page 227 - Becoming Metric Wise

218 Becoming Metric-Wise

Table 7.6 Calculation of a g-index
Rank Publication (date) # citations Cumulative number Squared
of citations rank
1 A (2010) 8 8 1
2 B (2013) 5 13 4
3 C (2011) 5 18 9
4 D (2011) 4 22 16
5 E (2008) 4 26 25
6 F (2014) 1 27 36
7 G (2010) 0 27 49

An example. We consider again Table 7.2 and add the information
necessary to determine its g-index, see Table 7.6.
2
As the articles ranked 1 to 5 have together at least 5 5 25 citations,
2
namely 26, and the articles ranked 1 to 6 have strictly less than 6 5 36
citations (they have 27 citations), this set has a g-index equal to 5.
The use of a square in this definition is inspired by the fact that a set
2
with h-index h has received together at least h citations. Consider for
instance [4, 4, 4, 4, 0, 0]. This set has h-index 4; the total number of cita-
tions is 16 and its g-index is also 4. From this it also follows that for a
given set, we have g $ h.
As for the h-index one may say that the first g articles form the
g-core, again ranking in antichronological order if need be.
What happens if a list of T articles has together strictly more than T 2
citations? This is illustrated in Table 7.7. In this case one adds “fictitious”
articles with zero citations until the g-index can be calculated. The fact
that it is not bounded by the number of publications can be considered
an advantage of the g-index (Gla ¨nzel, 2006).
Before discussing a few other h-type indices we consider the question:
Which one of the two, the h-index or the g-index, is the best one?
Egghe being the originator of the g-index naturally prefers the g-index.
However, we leave it to the readers to make up their mind, or to decide
whether this is a meaningless question. Either way, here are two examples,
illustrating two opposite cases:
X 1 5 [15, 10, 5, 3] and X 2 5 [3,3,3,0,0,0] have the same h-index,
namely 3, but different g-indices: g(X 1 ) 5 5 while g(X 2 ) 5 3.
Consider now Y 1 5 [60,4,0,0,0,0] and Y 2 5 [15,15,12,12,8,7,7,3,1].
These scientists have the same g-index: g(Y 1 ) 5 g(Y 2 ) 5 8, but different
h-indices: h(Y 1 ) 5 2 and h(Y 2 ) 5 7.