Page 180 - Becoming Metric Wise

172 Becoming Metric-Wise

totals are always equal to one). Rows of dangling journals are replaced by the
article vector a. Next one defines a new matrix P as:
P 5 αH 1 ð1 2 αÞA (6.13)

where A is a matrix consisting of the same rows, each consisting of the arti-
cle vector. The Greek letter α represents an adaptable parameter. In the
calculation of the Eigenfactor Score α is taken equal to 0.85. The occur-
rence of this parameter implies that, by adapting α, an infinite number of
eigenfactors is feasible. Let now π be the eigenvector of P for which the
equality π 5 πP holds (hence, with corresponding eigenvalue equal to 1).
This vector π is called the influence vector. It contains the scores used to
weight the citations in H. Finally, the eigenfactor vector r is obtained as:

πH
100 (6.14)
r 5 P
ð πHÞ
i i
The Eigenfactor Score of journal j is the j-th component of this vec-
tor. It can be considered as the sum of all normalized citations received
from citing journals, weighted by the Eigenfactor Scores of these citing
journals. Eigenfactor Scores are normalized in such a way that their sum
(for the whole citation database) is equal to 100.
The AIS of a journal is equal to its Eigenfactor Score divided by the
number of articles published during the 5-year publication window and
normalized in such a way that the average value for the whole database is
equal to 1. Hence the AIS of a journal is a normalized Eigenfactor Score
per published article.
The SJR (SCImago Journal Ranking) indicator, as made available in
SCImago Journal & Country Rank, is also a variant on the Pinski-Narin
or Google approach. Gonza ´lez-Pereira et al. (2010) refer to this class of
indicators as prestige indicators. Also the SJR indicator is directly inspired
by the journal status as described in (Bollen et al., 2006).

6.9.3 Advantages of the Eigenfactor Score and Related
Journal Indicators (Franceschet, 2010b)

• Citations are weighted according to the importance of citing journals.
Hence, the Eigenfactor Score and related indicators can be considered
prestige indicators, see also Gonzalez-Pereira et al. (2010), while the class
of synchronous or diachronous impact factor are rather popularity scores.
• The AIS takes the length of reference lists into account. Hence receiv-
ing a citation from a journal with short reference lists is considered