Page 143 - Becoming Metric Wise

134 Becoming Metric-Wise

The major theoretical criticism of the concept of bibliographic
coupling comes from Martyn (1964). He contends that a bibliographic
coupling unit is not a valid measure of relationship because the fact that
two papers have a common reference is no guarantee that both papers are
referring to the same piece of information.
Finally, using the notation of Subsection 5.9.3 we note that the biblio-
graphically coupling strength between documents d i and d j , with C the
citation matrix of the field including d i and d j is given by:
n
X
t
c ik c jk 5 C C Þ (5.8)
ð
ij
k51
Indeed, terms in the sum on the left hand side are zero or one. The value
one only happens in the case that document k is cited by document d i and
by document d j . These occurrences are added, yielding the bibliographic
t
t
coupling strength. Finally C C Þ 5 P n ðCÞ : C Þ 5 P n c
ð
ð
ij k51 ik kj k51 ik c jk .To
make this less abstract, we include a concrete example. Consider a matrix M.
Itscolumns denotereferencesand itsrowsarticles(Art1,Art2, Art3,and
Art4). A value 1incell(k,l) means that article k has article l among its refer-
ences; a zero value in cell (k,l) means that this is not the case.
0 1
1 1 1 1 1
B 0 0 1 1 0 C
M 5 B C :
@ 1 0 0 0 1 A
0 1 1 1 0

0 1
1 0 1 0
B 1 0 0 1 C
t
Its transpose M is: B 1 1 0 1 C
C
B
B C
@ 1 1 0 1 A
1 0 1 0
t
The multiplication M M gives the bibliographic coupling matrix of
the articles Art1 to Art4. This matrix is symmetric by definition.
0 1
5 2 2 3
2 2 0 2 C
B
t
M M 5 B C :
@ 2 0 2 0 A
3 2 0 3