Page 177 - Becoming Metric Wise

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Journal Citation Analysis

Table 6.10 Ranked table for the calculation of the
h-index of a journal

Rank Received citations
1 19
2 16
3 10
4 6
5 5
6 4
7 3
8 3
9 2
10 2
11 1
12 1

6.9 INDICATORS THAT TAKE THE IMPORTANCE
OF THE CITING JOURNAL INTO ACCOUNT

One could argue that a citation received from an important journal car-
ries more weight than a citation received from a less important journal
(whatever the words “important” and “unimportant” may stand for).
Based on an idea from Kochen (1974) this was elaborated by Pinski and
Narin (1976). In this approach citations are weighted by the impact of
the citing journal. In this way these colleagues were the first to break
through the “equally weighted citations” wall.
The underlying idea of their approach is the calculation of an eigen-
vector associated with the largest eigenvalue of a linear mapping (or
equivalently, a matrix). It is this idea that has been re-invented (with
some clever adaptations) by Brin and Page (1998) and applied to links on
the Internet, leading to the Google algorithm also known as the
PageRank algorithm.
Determining eigenvalues and eigenvectors of large matrices is not
straightforward. Pinski & Narin proposed the so-called “power method,”
a well-known numerical algorithm.

6.9.1 A Short Description of the Pinski-Narin Algorithm
Let C 5 (C i,j ) be a citation matrix. In our case C i,j denotes the number
of citations given by journal i to journal j.Let S i be the number of
references in journal i.Weconstruct anew matrix M 5 (M i,j ), where