Page 144 - Becoming Metric Wise

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Publication and Citation Analysis

Checking, we see that the value 3 in cell (1,4) indicates that articles 1
and 4 have a bibliographic coupling strength equal to 3. This is indeed
the case (see matrix M). The values on the diagonal show the number of
references of each article.
We propose the following (somewhat tricky) exercises on biblio-
graphic coupling and relative bibliographic coupling.
Article A has 9 references; the relative bibliographic coupling of arti-
cles A and B is 7/13. How many references does article B have?
Solution
There are 7 references in the intersection of the two reference lists,
hence there are 2 references in A which are not references of B. Hence
there are 4 references of B which are not references of A. Consequently
B has 11 references.
Try now to solve the following exercise. Article A has 6 references;
the relative bibliographic coupling of articles A and B is 0.1666667
(rounded). How many references does article B have? Hint: there are six
different solutions.
Solution
We must realize that the number 0.1666667 is equal to 1/6 5 2/
12 5 3/18 5 4/24 5 5/30 5 6/36 5 7/42 5 .. . Writing these fractions
we see the exact number of references in the intersection of the two
reference lists. As A has a total of 6 references 7/42 (referring to the
case of 7 references in the intersection) cannot occur. This reasoning
leads to six different solutions presented in Table 5.6. Note that, for
the first problem, there was a unique solution, contrary to the sec-
ond one.

Table 5.6 Solution of the bibliographic coupling problem
Number of articles Joint Number of articles Length of B’s
in A’s reference list, references in B’s reference list, reference list
not belonging to B’s not belonging to A’s
reference list reference list

5 1 0 1
4 2 6 8
3 3 12 15
2 4 18 22
1 5 24 29
0 6 30 36