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136 Becoming Metric-Wise

5.10.2 Cocitations
A Soviet information scientist (Irina Marshakova) and an American one
(Henry Small) independently proposed the same variation on biblio-
graphic coupling. Small (1973) and Marshakova (1973) both suggested
cocitation of documents as a method of measuring relationships between
documents.
Two documents are said to be cocited when they both appear in the
reference list of the same document. That is, if the relation Cit(A;B,C)
holds, documents B and C are cocited. The cocitation frequency is
defined as the frequency with which two documents are cited together.
Thus, while bibliographic coupling focuses on groups of papers which
cite the same source document, cocitation focuses on references which
frequently come in pairs (see Fig. 5.6). In the Soviet (Russian) literature
bibliographic coupling is said to be retrospective while cocitation is called
prospective coupling (Marshakova, 1973).
Alternatively, by using the language of set theory, one can define the
cocitation frequency of two documents X and Y as follows. If S(X) is the
set of papers citing document X and S(Y) is the set of papers citing docu-
ment Y then S(X) - S(Y), the intersection of S(X) and S(Y), is the set of
papers citing X and Y. If this set is nonempty then X and Y are cocited.
The number of elements in this intersection, denoted as #(S(X) - S(Y))
is the cocitation frequency of X and Y. Of course, to be precise one must
also mention a citation window. It makes quite a difference if one studies
cocitation over 1 year or over a decade.
The relative cocitation frequency can easily be defined using the nota-
tion of set theory. It is:
# SðXÞ - SðYÞÞ
ð
(5.9)
ð
# SðXÞ , SðYÞÞ
Of course the notions of bibliographic coupling and cocitation can be
used for any type of documents (not just journal articles) such as books.
The cocitation strength of two documents can never decrease.
Bibliographic coupling and cocitation of articles are not equivalence
relations as they are not transitive in general. This is somewhat unfortu-
nate as an equivalence relation leads to natural groups (equivalence clas-
ses). As there are no natural groups and obtaining nonoverlapping groups
of related documents is highly desirable, groupings are obtained in a sub-
jective manner, for instance by using a clustering algorithm, see e.g.,