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Publication and Citation Analysis

defined as follows. Let X and Y be two documents. If R(X)denotes the
set of papers in the reference list of document X and R(Y)the set
of papers in the reference list of Y then R(X) - R(Y), the intersection
of R(X)and R(Y), is the set of papers belonging to these two reference
lists. If this set is nonempty then X and Y are bibliographically coupled.
The number of elements in this intersection, denoted as #(R(X) - R
(Y)) is the bibliographic coupling strength of X and Y.The relative
bibliographic coupling strength frequency can easily be defined using
the notation of set theory. It is:
ð RðXÞ - RðYÞÞ
(5.7)
ð RðXÞ , RðYÞÞ
We note that the bibliographic coupling strength of two documents is
at most equal to the length of the smallest reference list of the two. The
bibliographic coupling strength of two documents is fixed once the most
recent one of the two is published, but the number of documents to
which a given document is bibliographically coupled may increase over
time and has no theoretical limit.
Bibliographic coupling is a symmetric relation: if document d 1 is bib-
liographically coupled to document d 2 then automatically document d 2 is
bibliographically coupled to document d 1 , and this with equal absolute
and relative coupling strength. One may agree, as in (Egghe & Rousseau,
1990) that a document is bibliographically coupled to itself, making the
bibliographic coupling relation reflexive. Yet, this relation is not necessar-
ily transitive: If d 1 and d 2 are bibliographically coupled and also d 2 and d 3
are bibliographically coupled then there is no reason to conclude that d 1
and d 3 are bibliographically coupled (readers can easily provide an exam-
ple themselves). Contrary to what is claimed in (Egghe & Rousseau,
1990, p. 238) the relation is transitive if it is known that documents d 1 ,
d 2 , and d 3 have exactly one reference.
Kessler (1963) saw bibliographic coupling in the first place as a retrieval
tool. Knowing that a paper P 0 is relevant to a user’s search, an automatic
retrieval system would also retrieve (or suggest to retrieve) all papers that
are bibliographically coupled to P 0 . This idea has been taken up by the
WoS as a suggestion to expand the search with closely related papers (by
bibliographically coupled papers with a high coupling strength).
Kessler remarks that a paper’s set of articles with which it is biblio-
graphically coupled can be considered its “logical references.” This might
be particularly true at the moment of its publication.