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directly cited a retracted article. Citation counts and whether it is evident that the
citers were aware of the status of retracted articles are the most commonly studied
topics.
Given a published article a
t
o
, retracted or not, a citation path between a
subsequently published article a
t
k
and the original article can be defined in terms
of pairwise citation relations as follows: a
t
o
a
t
1
a
t
k
,where
denotes
a direct citation reference, t
i
<t
j
if
i
<
j
, and the length of each segment of the path
is minimized. In other words, a
t
i
a
t
i
C
1
means a
t
i
C
1
has no direct citation to any
of the articles on the path prior to a
t
i
. The length of a citation path is the number
of direct citation links included in the path. Existing studies of citations to retracted
articles are essentially limited to citation paths that contain one step only. Longer
citation paths originated from a retracted article have not been studied. It is clear
that the retraction of the first article is equivalent to the removal of the first article
from a potentially still growing path such as a
t
o
a
t
1
a
t
k
because newly
published articles may unknowingly cite the last article a
t
k
without questioning the
validity of the potentially risky path. By
k
-degree post-retraction citation analysis,
we introduce a study of such paths formed by
k
pairwise direct citation links as in
a
t
o
a
t
1
a
t
k
:
8.3.1.2
Citation Networks Involving Retracted Articles
Over the recent years, tremendous advances have been made in scientometrics
(Boyack and Klavans
2010
; Leydesdorff
2001
; Shibata et al.
2007
; Upham et al.
2010
), science mapping (Chen
2006
; Cobo et al.
2011
;Small
1999
;vanEck
and Waltman
2010
), and visual analytics (Pirolli
2007
; Thomas and Cook
2005
).
Existing studies of citations to retracted articles have not yet incorporated these
relative new and more powerful techniques. Vice versa researchers who have access
to the new generation of analytic tools have not applied these tools to the analysis
of citation networks involving retracted articles.
8.3.1.3
Citation Context
It is important to find out how much a citing article's authors know about the
current status of a retracted article when they refer to the retracted article. Previous
studies have shown that this is not always clear in text. A retracted article may have
been cited by hundreds of subsequently published articles. Manually examining
individual citation instances is time consuming and cognitively demanding. It is
an even more challenging task for analysts to synthesize emergent patterns from
individual citation instances and discern changes in terms of how a retracted article
has been cited over an extensive period of time because it is known that retracted
articles can be cited continuously for a long time after the retraction.
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