Page 215 - Becoming Metric Wise

206 Becoming Metric-Wise

3. The collaborative coefficient (Ajiferuke et al., 1988)
A f j
P
CC 5 1 2 j51 j (7.3)
N
The CC is one minus the average credit awarded to each author if
complete-normalized fractional counting (5.6.3) is used.
4. The normalized CC (Egghe, 1991)

P A f j !
A j51 j

CC 5 1 2 (7.4)
A 2 1 N
Arguments can be put forward to conclude that CC is better than

CC , yet other arguments may lead to the conclusion that CC is the

better one (Rousseau, 2011). If A is large the difference between CC and

CC is in practice negligible.
Soon after the introduction of the CC Egghe (1991) and Englisch
(1991) noted that this indicator does not provide detailed information
and yields the same value in collaboration cases for which one would like
to make a distinction. Consequently, Egghe proposed a list of eight prin-
ciples which an acceptable collaboration measure should satisfy (one of
these being normalization). Yet, he showed that CC does not satisfy

some of the other natural principles. After a thorough investigation he
succeeded in finding a—rather sophisticated— measure, denoted as γ
(gamma), which satisfies all his requirements. This measure, Egghe’s
gamma measure for collaboration, is defined as:
s 1 t
γ 5 where (7.5)
2

0 1 2
v ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
B A u q C
1 B X u X C
s 5 B t x ðjÞ C (7.6)
2 2 0
A A21ð B j51 i;i C
0
i; i 51 A
Þ N @
i 6¼ i 0
and
! 2
1 X q ffiffiffiffiffiffi
t 5 x ðjÞ (7.7)
2 2 2 i;i 0
A A21ð Þ Nk
i;i ;j
0