ARTICLE DE RECHERCHE

A multidimensional framework for characterizing
the citation impact of scientific publications

Yi Bu1,2

, Ludo Waltman3

, and Yong Huang4

1Department of Information Management, Peking University, Beijing, Chine
2Center for Complex Networks and Systems Research, Luddy School of Informatics,
Computing, and Engineering, Indiana University, Bloomington, IN, Etats-Unis
3Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands
4School of Information Management, Wuhan University, Wuhan, Hubei, Chine

Mots clés: breadth, citation impact, dependence, depth, independence, publication

ABSTRAIT

The citation impact of a scientific publication is usually seen as a one-dimensional concept. Nous
introduce a multidimensional framework for characterizing the citation impact of a publication.
In addition to the level of citation impact, quantified by the number of citations received by a
publication, we also conceptualize and operationalize the depth and breadth and the
dependence and independence of the citation impact of a publication. The proposed framework
distinguishes between publications that have a deep citation impact, typically in a relatively
narrow research area, and publications that have a broad citation impact, probably covering a
wider area of research. It also makes a distinction between publications that are strongly
dependent on earlier work and publications that make a more independent scientific
contribution. We use our multidimensional citation impact framework to report basic
descriptive statistics on the citation impact of highly cited publications in all scientific
disciplines. En outre, we present a detailed case study focusing on the field of scientometrics.
The proposed citation impact framework provides a more in-depth understanding of the citation
impact of a publication than a traditional one-dimensional perspective.

1.

INTRODUCTION

Measuring the citation impact of scientific publications is an important topic in bibliometric and
scientometric research. Many different citation impact indicators, calculated based on the cita-
tions received by a publication, have been proposed (Waltman, 2016), ranging from the raw
citation count of a publication to field-normalized indicators (par exemple., Radicchi, Fortunato, &
Castellano, 2008; Waltman & Van Eck, 2019; Waltman, Van Eck et al., 2011), recursive
PageRank-inspired indicators (par exemple., Chen, Xie et al., 2007; Walker, Xie et al., 2007; Waltman
& Yan, 2014) as well as indicators that take into account attributes derived from the full text
of citing publications (par exemple., Ding, Liu et al., 2013; Wan & Liu, 2014; Zhu, Turney et al.,
2015). These approaches have in common that they all regard the citation impact of a publica-
tion as a one-dimensional concept. In this paper, we propose a multidimensional perspective on
the citation impact of a publication. We argue that, in addition to the level of citation impact,
there are other relevant aspects of the citation impact of a publication that can be derived
from a citation network.

un accès ouvert

journal

Citation: Bu, Y., Waltman, L., & Huang, Oui.
(2021). A multidimensional framework
for characterizing the citation impact of
scientific publications. Quantitative
Science Studies, 2(1), 155–183. https://
doi.org/10.1162/qss_a_00109

EST CE QUE JE:
https://doi.org/10.1162/qss_a_00109

Reçu: 2 Août 2020
Accepté: 22 Novembre 2020

Auteur correspondant:
Yi Bu
buyi@pku.edu.cn

Éditeur de manipulation:
Vincent Larivière

droits d'auteur: © 2021 Yi Bu, Ludo
Waltman, and Yong Huang. Published
under a Creative Commons Attribution
4.0 International (CC PAR 4.0) Licence.

La presse du MIT

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A multidimensional framework for characterizing the citation impact of scientific publications

To illustrate this point, consider two publications, A and B. As shown in Figure 1, these pub-
lications have each received five citations. If we just count the citations received by A and B, le
publications have the same citation impact. Cependant, the publications citing A also cite each
other and therefore seem to be closely related, while the publications citing B do not cite each
other and therefore seem to be quite unrelated to each other. Ainsi, A and B have the same level
of citation impact, but they differ fundamentally in the way in which they have an impact on
other publications. We say that publication A has a deep citation impact because the publica-
tions by which it is cited also cite each other, suggesting that these publications all belong to a
relatively narrow research area in which they build on each other in a cumulative way. In con-
trast, we say that publication B has a broad citation impact because it is cited by publications that
do not cite each other. As the publications citing B do not cite each other, they do not seem to
build on each other and they may cover a relatively wide research area. To capture the differ-
ence in citation impact between A and B, we propose an approach for quantifying the depth and
breadth of the citation impact of a publication.

We are also interested in the dependence of a publication’s citation impact on earlier pub-
lications. In Figure 2, publications A and B have both received five citations, and they both have
three references. All publications citing A also cite each of A’s references, while the publications
citing B do not cite B’s references. Ainsi, the citation impact of A seems to depend strongly on
earlier publications, namely those cited by A. It is likely that A is a follow-up study of these earlier
publications. In contrast, B seems to have a much more independent citation impact, as publi-
cations citing B do not cite the references of B.

We propose to conceptualize and operationalize the citation impact of a publication in a
multidimensional framework that focuses on the level, the depth and breadth, et le

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Chiffre 1. Deep and broad citation impact. Nodes represent publications and edges represent citation relations. Publications A and B (c'est à dire., le
focal publications) have both received five citations. All publications citing A (A1, A2, A3, A4, and A5) also cite each other, while publications
citing B (B1, B2, B3, B4, and B5) do not cite each other. Therefore A has a deep citation impact, while B has a broad citation impact.

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Chiffre 2. Dependent and independent citation impact. Nodes represent publications and edges
represent citation relations. Publications A and B (c'est à dire., the focal publications) have both received
five citations, and they both have three references. All publications citing A (A1, A2, A3, A4, et
A5) also cite each of the references of A (A6, A7, and A8), while publications citing B (B1, B2, B3,
B4, and B5) do not cite references of B (B6, B7, and B8). Therefore A has a citation impact that is
strongly dependent on earlier publications, while B has an independent citation impact.

dependence and independence of citation impact. In a traditional one-dimensional perspective
on citation impact, only the level of citation impact is considered. Beyond the level of citation
impact, no insights are obtained into the way in which a publication has an impact on other
publications. By introducing the dimensions of depth and breadth and of dependence and
independence, our proposed framework aims to offer a more in-depth understanding of the
citation impact of a publication. Our focus is on citation impact at the level of individual pub-
lications, but the insights that are obtained at this level may also be used at aggregate levels, pour
instance at the level of researchers.

The organization of this paper is as follows. In Section 2, we provide a brief discussion of
related research. In Section 3, we describe the data that we use in our empirical analyses. Dans
Sections 4–6, we introduce the conceptualization and operationalization of the different dimen-
sions of our citation impact framework (c'est à dire., level, depth and breadth, and dependence and
independence) and we report some basic descriptive statistics for each of these dimensions.
In Section 7, we present a case study in which we apply our citation impact framework to pub-
lications in the field of scientometrics. Enfin, in Section 8, we provide some further discussion
and we summarize our conclusions.

2. RELATED RESEARCH

The idea of analyzing citation relations between publications that cite a focal publication has
been explored in a number of earlier studies. Clough, Gollings et al. (2015) compared the num-
ber of citations given to a publication in a citation network with the number of citations given to
the same publication in the transitive reduction of the citation network. According to Clough

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et coll., the transitive reduction can be used to get “an indication that results in a paper were used
across a wide number of fields.” Huang, Bu et al. (2018, 2020) analyzed so-called citing
cascades, defined as the citation network of a focal publication and its citing publications. Dans
particular, they studied citation relations between citing publications. The citation impact frame-
work proposed in the current paper partly builds on the ideas explored by Huang et al.

The notion of dependence introduced in our citation impact framework is closely related to
the concepts of development and disruption proposed by Funk and Owen-Smith (2017) et
used by Wu, Wang, and Evans (2019). Wu et al. investigated an indicator that provides a proxy
of whether a publication tends to “disrupt” or “develop” science by taking into consideration the
publication’s references and its citing publications, as well as the citations between all these
publications. For a given focal publication, they defined “type i” publications as those that cite
the focal publication but not the references of the focal publication, “type j” publications as
those that cite both the focal publication and the references of the focal publication, and “type k”
publications as those that cite the references of the focal publication but not the focal publi-
cation itself. Based on content-level validation, expert interviews, and some other evaluations,
the indicator adopted by Wu et al. showed good performance in assessing the degree to which a
publication “disrupts” or “develops” science. Encore, a follow-up study by Bornmann and Tekles
(2019un) suggested that the length of the time window for calculating the disruptiveness of
publications may affect the results. En outre, a case study by Bornmann and Tekles (2019b)
questioned the ability of the disruptiveness indicator to identify disruptive publications in the
journal Scientometrics. En outre, Bornmann, Devarakonda et al. (2020un, 2020b) compared
the disruptiveness indicator with other related indicators, in particular those proposed by Wu
and Yan (2019) and by an earlier version of the current paper. Bornmann et al. (2020un) argued
that different indicators tend to represent similar dimensions.

The notion of dependence introduced in the current paper is also related to the idea of
originality proposed by Shibayama and Wang (2020). Both approaches consider the number
of citations from the citing publications of a focal publication to its references.

Building on the idea of citing cascades proposed by Huang et al. (2018), Mohapatra, Maiti
et autres. (2019) introduced a method for pruning the citing cascade of a focal publication p. Pour
each citing publication q of p, only the longest path between q and p is retained in the pruned
réseau. Based on the pruned network, Mohapatra et al. defined several indicators, in particular
depth (c'est à dire., the length of the longest path between the focal publication and the leaf nodes in the
réseau) and width (c'est à dire., the maximum number of nodes at a given level in the network). Ils
assumed that a publication has the most “influential” impact when the values of depth and width
are equal. This assumption lacks a clear conceptual foundation, but it was tested empirically
using “Test of Time Awards.” Importantly, as will become clear in Section 5, the definitions of
depth and breadth that we propose in the current paper are quite different from the definitions of
depth and width introduced by Mohapatra et al.

3. DATA

The empirical analyses presented in this paper were carried out using data extracted from the in-
house version of the Web of Science ( WoS) database available at the Centre for Science and
Technology Studies (CWTS) at Leiden University. We made use of the Science Citation Index
Expanded, the Social Sciences Citation Index, and the Arts & Index des citations en sciences humaines. Nous
considered only publications of the document types article, revoir, and letter. Our data covers
36.2 million publications that appeared between 1980 et 2017 et 699.3 million citation
relations between these publications.

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A multidimensional framework for characterizing the citation impact of scientific publications

Our analyses focus on highly cited publications in the period 2000–2017, where a highly
cited publication is defined as a publication that has received at least 100 citations at the end
de 20171. In total, 550,747 highly cited publications in the period 2000–2017 were identified.
For these publications, we calculated the citation impact indicators defined in the next sections.
In the calculation of the indicators of dependence and independence, we considered only
references to publications included in our data (73.1% of all references). References to publica-
tions not included in the data, typically publications not indexed in the WoS database, were not
taken into account. This is why our analyses focus on publications from the period 2000–2017
and why publications from the period 1980–1999 are not considered. The calculation of
our indicators of dependence and independence for publications from the period 1980–1999
would be affected by the fact that many references in these publications point to literature that
appeared before 1980 and that is not included in our data.

Using the algorithmic methodology introduced by Waltman and Van Eck (2012), publications in
the WoS database in the period 2000–2017 were clustered based on citation relations. We obtained
4,047 clusters of publications. Clusters are nonoverlapping. Each publication belongs to only one
cluster. Le 4,047 clusters were grouped into the following five broad scientific disciplines2:

(cid:129) Biomedical and health sciences (BHS; 291,342 highly cited publications)
(cid:129) Life and earth sciences (LES; 73,113 highly cited publications)
(cid:129) Mathematics and computer science (MCS; 10,475 highly cited publications)
(cid:129) Physical sciences and engineering (PSE; 148,521 highly cited publications)
(cid:129) Social sciences and humanities (SSH; 27,149 highly cited publications)

4. LEVEL OF CITATION IMPACT

As already mentioned, our citation impact framework distinguishes between three dimensions of
the citation impact of a publication, namely level, depth and breadth, and dependence and in-
dependence. Dans cette section, we discuss the dimension of the level of citation impact. The depth
and breadth and the dependence and independence dimensions are discussed in Sections 5
et 6, respectivement.

4.1. Conceptualization and Operationalization

The level of citation impact of a publication reflects how much impact the publication has had
on other publications. We operationalize this by the number of citations a publication has re-
ceived, denoted by CP. The larger the number of citations a publication has received, the higher
the level of citation impact of the publication. The level of citation impact represents the tradi-
tional perspective on the citation impact of a publication.

4.2. Descriptive Statistics

We now report some descriptive statistics for the CP indicator. Statistics are presented for each of
the five broad scientific disciplines and for all disciplines together (labeled “ALL” in the tables
and figures in this paper). The statistics are based on the 550,747 highly cited publications

1 The relative indicators that will be introduced in Sections 5 et 6 provide meaningful results only for publi-
cations that have received a substantial number of citations. Most of our analyses therefore focus on highly
cited publications.

2 For more details, see https://www.leidenranking.com/information/fields.

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A multidimensional framework for characterizing the citation impact of scientific publications

Tableau 1. Median value of the CP indicator for different disciplines

CP

BHS
150

LES
144

MCS
144

PSE
149

SSH
149

ALL
148

discussed in Section 3. For each discipline, Tableau 1 reports the median value of the CP indicator.
Chiffre 3 shows the underlying distribution. As expected, the distribution of the CP indicator is
highly skewed. The horizontal axis in Figure 3 therefore has a logarithmic scale.

The distribution of the CP indicator is very similar for different disciplines. Normally, to obtain
similar citation distributions for different disciplines, a rescaling needs to be performed that nor-
malizes for differences between disciplines in the average level of citation impact (Radicchi
et coll., 2008; Waltman, Van Eck, & Van Raan, 2012). Cependant, we consider only highly cited
publications (c'est à dire., the tail of the citation distribution). For these publications, there turns out to
be no need to perform a rescaling.

5. DEPTH AND BREADTH OF CITATION IMPACT

To motivate the idea of the depth and breadth and the dependence and independence of the ci-
tation impact of a publication, we consider the following article dealing with a topic in the field of
webometrics: Thelwall (2001). For simplicity, we refer to this article as publication P. In our data,
P cites 43 publications and is cited by 107 publications. Some of the 107 citing publications
also cite other publications citing P. For a given publication citing P, R.[citing pub] denotes the
number of references to other publications citing P. Some publications citing P also cite
publications cited by P. For a given publication citing P, R.[cited pub] denotes the number of
references to publications cited by P.

The plots in Figure 4 show the distributions of R[citing pub] et R[cited pub] for the 107 pub-
lications citing P. As can be seen in the left plot, some publications citing P have a high value for
R.[citing pub]. There is even a publication that cites P and that also cites 42 other publications
citing P. Cependant, there are also publications that cite P and that do not cite any other publica-
tion citing P. De même, the right plot shows that some publications citing P have a high value for
R.[cited pub]. There is one publication that cites P and that also cites 22 publications cited by
P.. Inversement, some publications citing P do not cite any publication cited by P.

Chiffre 3. Cumulative distribution function of the CP indicator for different disciplines.

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A multidimensional framework for characterizing the citation impact of scientific publications

Chiffre 4. Distributions of R[citing pub] et R[cited pub] for the citing publications of publication P (Thelwall, 2001). Dashed vertical lines
indicate the mean of a distribution.

The two distributions discussed in the above example provide important information about
the citation impact of a publication. In the rest of this section, we use the distribution of R[citing
pub] to quantify the depth and breadth of a publication’s citation impact. In Section 6, the dis-
tribution of R[cited pub] is used to quantify the dependence and independence of a publication’s
citation impact.

5.1. Conceptualization and Operationalization

To understand the notion of the depth and breadth of the citation impact of a publication, nous
consider an example involving two publications, A and B. These publications have received the
same number of citations, and they therefore have the same level of citation impact. Cependant, UN
and B differ in how they have an impact on other publications. Publication A introduces an in-
novative new idea in a research field. Many publications in this field start to build on this idea.
These publications all cite A and many of them also cite each other. In contrast, outside the re-
search field of A, little attention is paid to the idea introduced in A and few citations are made to
UN. The situation is very different for B. This publication introduces a new software tool for car-
rying out certain statistical analyses. The tool turns out to be useful in many different research
fields. In all these fields, publications that use the tool cite B. Cependant, apart from the fact that
they use the tool introduced in B, these publications have little in common. They all deal with
different research problems. En général, publications citing B therefore do not cite each other.
In this example, A and B have an impact on other publications in very different ways. We say
that A has a deep citation impact while B has a broad citation impact. Chiffre 1 illustrates the
difference between the deep citation impact of A and the broad citation impact of B.

To quantify the depth and breadth of the citation impact of a publication, we propose the six
indicators summarized in Table 2. D'une part, we distinguish between indicators of depth
and indicators of breadth. On the other hand, we also make a distinction between absolute and
relative indicators. Absolute indicators scale with the level of citation impact of a publication,
while relative indicators are normalized for the level of citation impact. Relative indicators are
defined only for publications that have received at least one citation (c'est à dire., CP > 0). From a relative
point of view, depth and breadth are opposite concepts. A high depth implies a low breadth, et
vice versa. Ainsi, when a relative perspective is taken, depth and breadth can be seen as two
sides of the same coin. This is different when an absolute perspective is taken. From an absolute
point of view, a publication may have both a high depth and a high breadth, or it may have both a

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A multidimensional framework for characterizing the citation impact of scientific publications

Tableau 2.

Indicators of the depth and breadth of the citation impact of a publication

Breadth

CP(R.[citing pub] = 0)

Absolute indicators

Relative indicators

PCP(R.[citing pub] = 0)

Number of publications citing the focal
publication that do not cite other
publications citing the focal publication

Proportion of publications citing the focal

publication that do not cite other
publications citing the focal publication

Depth

CP(R.[citing pub] > 0)

PCP(R.[citing pub] > 0)

Number of publications citing the focal

publication that also cite other
publications citing the focal publication

Proportion of publications citing the focal

publication that also cite other publications
citing the focal publication

Depth

TR[citing pub]

MR[citing pub]

Total number of references in publications

citing the focal publication to other
publications citing the focal publication

Average number of references in publications

citing the focal publication to other
publications citing the focal publication

low depth and a low breadth. This means that, from an absolute point of view, depth and breadth
are conceptually distinct dimensions, even though they may be empirically correlated.

To further illustrate the distinction between absolute and relative perspectives, suppose that
we are interested in measuring poverty at the level of countries. Suppose that for each person
living in a country, we are able to determine whether this person is considered to be poor or not.
From an absolute point of view, we can then count the number of poor people and the number of
nonpoor people in a country. These are two conceptually distinct dimensions. Par exemple, si
there are 100,000 poor people in a country, this does not tell us anything about the number of
nonpoor people. There may be no nonpoor people at all in the country, but there may also be
100 million nonpoor people. Now consider the relative point of view. From this point of view,
we do not look at the number of poor people and the number of nonpoor people in a country, mais
we look at the proportion of poor people and the proportion of nonpoor people. These two pro-
portions are, bien sûr, two sides of the same coin. If we know the proportion of poor people in a
country (par exemple., 10%), we also know the proportion of nonpoor people (par exemple., 90%). Ainsi, the two
proportions represent the same conceptual dimensions. Our distinction between absolute and
relative indicators of depth and breadth of citation impact is analogous to the distinction
between absolute and relative measurements of poverty, but instead of countries and the people
living in them, we consider publications and the citations they receive.

Although we propose six indicators of the depth and breadth of the citation impact of a pub-
lication, our idea is that practical applications will probably use only one or two of them. Nous
now discuss the six indicators in more detail.

CP(R.[citing pub] = 0) and PCP(R.[citing pub] = 0) denote the number and the proportion of
publications citing the focal publication that do not cite other publications citing the focal
publication. CP(R.[citing pub] = 0) is an indicator of the absolute breadth of the citation impact
of the focal publication, while PCP(R.[citing pub] = 0) = CP(R.[citing pub] = 0)/CP is an indicator
of the relative breadth.

Consider publications A and B in Figure 1. CP(R.[citing pub] = 0) = 1 for A because A1 is the
only publication that cites A and that does not cite other publications citing A. CP(R.[citing pub] =
0) = 5 for B because none of the five publications citing B cites other publications citing B.
En outre, PCP(R.[citing pub] = 0) = 1/5 for A and PCP(R.[citing pub] = 0) = 5/5 = 1 for B.

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A multidimensional framework for characterizing the citation impact of scientific publications

The CP(R.[citing pub] = 0) and PCP(R.[citing pub] = 0) indicators show that B has a broader cita-
tion impact than A, both in absolute and in relative terms.

CP(R.[citing pub] > 0) and PCP(R.[citing pub] > 0) denote the number and the proportion of
publications citing the focal publication that also cite other publications citing the focal publi-
cation. CP(R.[citing pub] > 0) is an indicator of the absolute depth of the citation impact of the
focal publication, while PCP(R.[citing pub] > 0) = CP(R.[citing pub] > 0)/CP is an indicator of the
relative depth.

In Figure 1, CP(R.[citing pub] > 0) = 4 for A because A2, A3, A4, and A5 all cite A and also cite
other publications citing A. CP(R.[citing pub] > 0) = 0 for B because none of the five publications
citing B cites other publications citing B. En outre, PCP(R.[citing pub] > 0) = 4/5 for A and PCP
(R.[citing pub] > 0) = 0/5 = 0 for B. The CP(R.[citing pub] > 0) and PCP(R.[citing pub] > 0) indicators
show that A has a deeper citation impact than B.

Like CP(R.[citing pub] > 0) and PCP(R.[citing pub] > 0), TR[citing pub] and MR[citing pub] sont
indicators of, respectivement, the absolute and the relative depth of the citation impact of a publi-
cation. TR[citing pub] denotes the total number of references in publications citing the focal
publication to other publications citing the focal publication. MR[citing pub] = TR[citing
pub]/CP denotes the average number of references in publications citing the focal publication
to other publications citing the focal publication.

In Figure 1, TR[citing pub] = 10 for A because there are citation relations between all (5 × 4)/2 =
10 pairs of publications citing A. TR[citing pub] = 0 for B because the five publications citing B do
not cite each other. En outre, MR[citing pub] = 10/5 = 2 for A and MR[citing pub] = 0/5 = 0
for B. Like the CP(R.[citing pub] > 0) and PCP(R.[citing pub] > 0) indicators, the TR[citing pub] et
MR[citing pub] indicators show that A has a deeper citation impact than B.

Our absolute indicators of depth and breadth are related to indicators proposed by Huang
et autres. (2018). CP(R.[citing pub] = 0) is essentially equivalent to the number of “isolate endorsers”
in the terminology of Huang et al. De même, CP(R.[citing pub] > 0) is essentially equivalent to the
sum of the number of “late endorsers” and the number of “connectors.” TR[citing pub] is equiv-
alent to the number of direct citations between citing publications in the terminology of Huang
et autres. En outre, CP(R.[citing pub] = 0) is also similar, but not identical, to the citation counts
studied by Clough et al. (2015). These citation counts are obtained from the transitive reduction
of a citation network.

We do not intend to make a normative judgment by quantifying the depth and breadth of the
citation impact of a publication. From our point of view, a deeper citation impact is not neces-
sarily better than a broader citation impact, or the other way around. Cependant, we do believe
that the distinction between deep and broad citation impact is useful to get a more detailed un-
derstanding of the way in which a publication has an impact on other publications. We will
illustrate this in the case study presented in Section 7.

5.2. Descriptive Statistics

We now report some basic descriptive statistics for our indicators of the depth and breadth of the
citation impact of a publication. For each of our broad scientific disciplines, Tableau 3 reports the
median values of both the absolute and relative indicators. Chiffre 5 shows the underlying dis-
tributions. Because of the skewness of the distributions, the horizontal axes in Figure 5 have a
logarithmic scale. Table A1 in the Appendix reports correlations between the various indicators.

Based on the indicators of the absolute depth and breadth of citation impact (c'est à dire., CP(R.[citing
pub] = 0), CP(R.[citing pub] > 0), and TR[citing pub]), we observe that PSE publications tend

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A multidimensional framework for characterizing the citation impact of scientific publications

Tableau 3. Median values for different disciplines of the indicators of the depth and breadth of the citation impact of a publication

Absolute indicators

CP(R.[citing pub] = 0)

CP(R.[citing pub] > 0)

TR[citing pub]

Relative indicators

PCP(R.[citing pub] = 0)

PCP(R.[citing pub] > 0)

MR[citing pub]

BHS
48

102

361

BHS

0.30

0.70

2.31

LES
42

103

388

LES

0.27

0.73

2.56

MCS
53

93

277

MCS

0.34

0.66

1.78

PSE
40

109

442

PSE

0.24

0.76

2.81

SSH
57

95

280

SSH

0.35

0.65

1.79

ALL
46

104

378

ALL

0.28

0.72

2.42

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to have a relatively deep citation impact, while MCS and SSH publications tend to have a rel-
atively broad citation impact. This seems to suggest that PSE research is of a stronger cumulative
nature than MCS and SSH research. The relative indicators yield a similar picture (as is to be
expected, as the distribution of the level of citation impact is almost the same for all disciplines;
see Section 4.2).

6. DEPENDENCE AND INDEPENDENCE OF CITATION IMPACT

Dans cette section, we consider the dependence and independence of the citation impact of a
publication.

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6.1. Conceptualization and Operationalization

Two publications may have a similar level and a similar depth and breadth of citation impact, mais
nevertheless there may be an important difference in how they have an impact on other publi-
cations. Some publications may have an impact by building on earlier publications and by con-
tributing new scientific knowledge in a cumulative way. It is likely that these publications will be
cited together with publications that they build on and that they cite. These publications have a
citation impact that depends on earlier publications. We therefore say that these publications
have a dependent citation impact. This is illustrated by publication A in Figure 2. Other publi-
cations may have an impact without relying strongly on earlier publications. These publications
may introduce new ideas that have been developed relatively independently from earlier liter-
ature. These publications usually will not be cited together with publications that they cite. Nous
say that these publications have an independent citation impact. An illustration is provided by
publication B in Figure 2.

Our operationalization of the dependence and independence of the citation impact of a pub-
lication mirrors the operationalization of depth and breadth discussed in Section 5.1. Tableau 4
summarizes the six indicators that we propose for quantifying dependence and independence.
Like in the case of depth and breadth, we distinguish between absolute and relative indicators.
From a relative point of view, dependence and independence are opposite concepts. A high
dependence implies a low independence, and vice versa. From an absolute point of view,

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Chiffre 5. Cumulative distribution functions for different disciplines of the indicators of the depth and breadth of the citation impact of a
publication (gauche: absolute indicators; droite: relative indicators).

dependence and independence are conceptually distinct dimensions. From this viewpoint,
a publication may for instance have both a high dependence and a high independence.

In practical applications, there usually will be no need to use all six indicators of dependence
and independence. A typical application will probably use one or two of them. We now discuss
the six indicators in more detail.

CP(R.[cited pub] = 0) and PCP(R.[cited pub] = 0) denote the number and the proportion of
publications citing the focal publication that do not cite publications cited by the focal publica-
tion. CP(R.[cited pub] = 0) is an indicator of the absolute independence of the citation impact of
the focal publication, while PCP(R.[cited pub] = 0) = CP(R.[cited pub] = 0)/CP is an indicator of
the relative independence.

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Tableau 4.

Indicators of the dependence and independence of the citation impact of a publication

Independence

CP(R.[cited pub] = 0)

PCP(R.[cited pub] = 0)

Absolute indicators

Relative indicators

Number of publications citing the focal

publication that do not cite publications
cited by the focal publication

Proportion of publications citing the focal
publication that do not cite publications
cited by the focal publication

Dependence

CP(R.[cited pub] > 0)

PCP(R.[cited pub] > 0)

Number of publications citing the focal
publication that also cite publications
cited by the focal publication

Proportion of publications citing the focal
publication that also cite publications
cited by the focal publication

Dependence

TR[cited pub]

MR[cited pub]

Total number of references in publications

citing the focal publication to
publications cited by the focal publication

Average number of references in publications
citing the focal publication to publications
cited by the focal publication

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Consider publications A and B in Figure 2. CP(R.[cited pub] = 0) = 0 for A because all five
publications citing A also cite publications cited by A. CP(R.[cited pub] = 0) = 5 for B because
none of the five publications citing B also cites publications cited by B. En outre, PCP(R.[cited
pub] = 0) = 0/5 = 0 for A and PCP(R.[cited pub] = 0) = 5/5 = 1 for B. The CP(R.[cited pub] = 0) et
PCP(R.[cited pub] = 0) indicators show that B has a more independent citation impact than A,
both in absolute and in relative terms.

CP(R.[cited pub] > 0) and PCP(R.[cited pub] > 0) denote the number and the proportion of
publications citing the focal publication that also cite publications cited by the focal publication.
CP(R.[cited pub] > 0) is an indicator of the absolute dependence of the citation impact of the focal
publication, while PCP(R.[cited pub] > 0) = CP(R.[cited pub] > 0)/CP is an indicator of the relative
dependence.

In Figure 2, CP(R.[cited pub] > 0) = 5 for A because all five publications citing A also cite
publications cited by A. CP(R.[cited pub] > 0) = 0 for B because none of the five publications
citing B also cites publications cited by B. En outre, PCP(R.[cited pub] > 0) = 5/5 = 1 for A
and PCP(R.[cited pub] > 0) = 0/5 = 0 for B. The CP(R.[cited pub] > 0) and PCP(R.[cited pub] > 0)
indicators show that A has a more dependent citation impact than B.

Like CP(R.[cited pub] > 0) and PCP(R.[cited pub] > 0), TR[cited pub] and MR[cited pub] sont
indicators of, respectivement, the absolute and the relative dependence of the citation impact of a
publication. TR[cited pub] denotes the total number of references in publications citing the focal
publication to publications cited by the focal publication. MR[cited pub] = TR[cited pub]/CP
denotes the average number of references in publications citing the focal publication to publi-
cations cited by the focal publication.

In Figure 2, TR[cited pub] = 15 for A because there are citation relations between all 5 × 3 = 15
pairs of a publication citing A and a publication cited by A. TR[cited pub] = 0 for B because the
five publications citing B do not cite publications cited by B. En outre, MR[cited pub] =
15/5 = 3 for A and MR[cited pub] = 0/5 = 0 for B. Like the CP(R.[cited pub] > 0) and PCP(R.
[cited pub] > 0) indicators, the TR[cited pub] and MR[cited pub] indicators show that A has
a more dependent citation impact than B.

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Our absolute indicators of dependence and independence are related to statistics studied
by Wu et al. (2019). CP(R.[cited pub] > 0) and CP(R.[cited pub] = 0) are equivalent to, respectivement,
nj and ni in Figure 1 in Wu et al.

6.2. Descriptive Statistics

We now report some basic descriptive statistics for our indicators of the dependence and inde-
pendence of the citation impact of a publication. For each of our broad scientific disciplines,
Tableau 5 reports the median values of both the absolute and the relative indicators. Chiffre 6 shows
the underlying distributions. As in Figures 4 et 5, the horizontal axes have a logarithmic scale.
Table A2 in the Appendix reports correlations between the various indicators.

As can be seen in Table 5 and Figure 6, MCS publications have a relatively independent ci-
tation impact, both from an absolute and from a relative viewpoint. Compared with publications
in other disciplines, MCS publications have a citation impact that is less dependent on earlier
publications. Cependant, this may partly be an artifact of our data. As explained in Section 3, ref-
erences to publications not included in our data are disregarded. Publications in conference
procédure, which play an important role in MCS, are not included in our data. This may arti-
ficially decrease the dependence of the citation impact of MCS publications.

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7. CASE STUDY IN THE FIELD OF SCIENTOMETRICS

To demonstrate the value of our multidimensional framework for characterizing the citation im-
pact of publications, we now present a case study in which the framework is applied to publi-
cations in the field of scientometrics. As explained in Section 3, using an algorithmic
methodology, 4,047 clusters of publications were obtained, covering all scientific disciplines.
One of these clusters can be considered to represent the field of scientometrics. We selected the
14,464 publications in this cluster. This includes 182 highly cited publications, each of which
has received at least 100 citations. We calculated our citation impact indicators for all 14,464
publications. Below, we first discuss the absolute indicators and then the relative ones.

7.1. Absolute Indicators

Chiffre 7 presents scatter plots showing the correlation between the level of citation impact of the
scientometrics publications and the absolute depth and breadth and the absolute dependence

Tableau 5. Median values for different disciplines of the indicators of the dependence and independence of the citation impact of a publication

Absolute indicators

CP(R.[cited pub] = 0)

CP(R.[cited pub] > 0)

TR[cited pub]

Relative indicators

PCP(R.[cited pub] = 0)

PCP(R.[cited pub] > 0)

MR[cited pub]

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BHS
44

107

402

BHS

0.27

0.73

2.43

LES
40

105

375

LES

0.26

0.74

2.34

MCS
62

88

191

MCS

0.40

0.60

1.20

PSE
41

109

399

PSE

0.25

0.75

2.39

SSH
46

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328

SSH

0.28

0.72

1.99

ALL
43

107

390

ALL

0.27

0.73

2.36

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Chiffre 6. Cumulative distribution functions for different disciplines of the indicators of the dependence and independence of the citation
impact of a publication (gauche: absolute indicators; droite: relative indicators).

and independence of the citation impact of these publications. We use CP(R.[citing pub] > 0) et
CP(R.[citing pub] = 0) as indicators of, respectivement, absolute depth and absolute breadth, and CP
(R.[cited pub] > 0) and CP(R.[cited pub] = 0) as indicators of absolute dependence and absolute
independence. For each of the indicators, Table A3 in the Appendix lists the top 10 publications.
Based on Figure 7 and Table A3, we observe a substantial correlation between the indicators.
This is to be expected, as absolute indicators all depend on the number of citations that a pub-
lication has received. Nevertheless, there are also important differences between the indicators.

The article by Egghe (2006), in which the so-called g-index was introduced as an alternative
to the well-known h-index, offers a clear illustration of these differences. As can be seen in
Table A3, the CP indicator shows that this is the third most cited publication in the field of scien-
tometrics. In terms of the absolute depth of citation impact, this publication even ranks second,
while it ranks first in terms of the absolute dependence of citation impact. The prominent ranking

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Chiffre 7. Correlation between the level, the absolute depth and breadth (gauche), and the absolute dependence and independence (droite) of the
citation impact of scientometrics publications. Spearman’s rank correlation coefficient is used to quantify the strength of the correlation.

of Egghe’s article in terms of absolute depth and absolute dependence can be explained by the
important contribution made by this publication to a large stream of publications dealing with
the h-index and other bibliometric indicators of the performance of individual researchers. Many
of these publications cite each other, while they also often cite Egghe’s article as well as the
article by Hirsch (2005) in which the h-index was proposed. Looking at the top 10 publications
based on absolute breadth and absolute independence, it turns out the Egghe’s article is not even
included. Ainsi, Egghe’s article has a deep citation impact, but its citation impact is not very
broad. Aussi, the citation impact of Egghe’s article is strongly dependent on the citation impact of
the article by Hirsch. The independent citation impact of Egghe’s article is therefore limited.

Another example of a publication for which the different indicators yield quite different re-
sults is the article by Falagas et al. (2008), in which the strengths and weaknesses of a number of
bibliographic databases are discussed. As shown in Table A3, this article is ranked tenth in terms
of absolute depth, while it is ranked second in terms of absolute breadth. Ainsi, contrary to
Egghe’s article discussed above, the article by Falagas et al. has a very broad but not so deep
citation impact. Autrement dit, the article has been cited a lot, but many of the citing publica-
tions do not seem to be part of a coherent body of literature. Presumably, many researchers cite
the article to explain why they use a specific bibliographic database, without engaging more
substantively with the article. The lack of more substantive engagement may be partly due to
the fact that the article was published in a life sciences journal, not in a scientometric journal.
It is also remarkable that the article by Falagas et al. is ranked third in terms of absolute indepen-
dence, while it is not included at all in the top 10 publications based on absolute dependence.

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Encore, this is the opposite of what we observed for the article by Egghe. The independence of the
citation impact of the article by Falagas et al. seems to reflect the fact that this was one of the first
publications in which bibliographic databases were compared.

As already mentioned, the different absolute indicators are quite strongly correlated with
l'un l'autre, as they all depend on the number of citations a publication has received. Nous
now turn to relative indicators, for which the differences can be expected to be more substantial.

7.2. Relative Indicators

Relative indicators provide meaningful results only for publications that have received a sub-
stantial number of citations. In our analysis based on relative indicators, we therefore consider
only the 182 scientometrics publications that have received at least 100 citations3. Chiffre 8 pre-
sents two scatter plots that both show the relative depth and the relative dependence of the
citation impact of the 182 highly cited publications. In the top plot, PCP(R.[citing pub] > 0) et
PCP(R.[cited pub] > 0) are used as indicators of, respectivement, relative depth and relative depen-
dence. In the bottom plot, we instead use the MR[citing pub] and MR[cited pub] indicators. We do
not consider indicators of relative breadth and relative independence. From a relative point of
voir, breadth is the direct opposite of depth and likewise independence is the direct opposite
of dependence4. Donc, it is sufficient to look only at depth and dependence.

The four publications denoted by P1, P2, P3, and P4 in Figure 8 were selected for a more
detailed analysis. We selected a publication with a low depth and a low dependence (P1), un
publication with a high depth and a low dependence (P2), a publication with a low depth
and a high dependence (P3), and a publication with a high depth and a high dependence
(P4). We chose publications with which we are sufficiently familiar ourselves, so that we are
able to offer a detailed interpretation of the citation impact of the selected publications.

Tableau 6 lists the four selected publications and reports their number of citations and number of
références. En outre, for each of the selected publications, Chiffre 9 shows the distribution of
the number of citations from publications citing the selected publication to other publications
citing the selected publication (c'est à dire., the distribution of R[citing pub]) as well as the distribution of
the number of citations from publications citing the selected publication to publications cited by
the selected publication (c'est à dire., the distribution of R[cited pub]). We note that publication P4 is
identical to publication P discussed in Section 5. Using the information provided in Figures 8
et 9 and Table 6, we now offer an in-depth interpretation of the citation impact of the four
selected publications.

Publication P1 is the article that introduced the popular VOSviewer software for visualizing
bibliometric networks (Van Eck & Waltman, 2009). VOSviewer is used in a large number of
publications in many different research fields. Publications that use VOSviewer often cite P1.
In our data, P1 has been cited 273 times. Publications that use VOSviewer typically present a
bibliometric analysis of the scientific literature in a specific research field or on a specific re-
sujet de recherche. Such publications use VOSviewer as a tool for bibliometric visualization. Ils
usually do not aim to develop new bibliometric methods or tools. Par conséquent, most publica-
tions citing P1 do not contribute to the methodological literature on bibliometric visualization.
Publications citing P1 therefore tend to refer only sparsely to other publications on bibliometric
visualization. This is reflected by the relatively low depth and dependence of P1. MR[citing pub]

3 The full results of the analysis are available in a data repository (Bu & Waltman, 2020).
4 We emphasize that this is the case only when a relative point of view is taken. As discussed in Sections 5.1 et

6.1, this is not the case when an absolute point of view is taken.

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Chiffre 8. Correlation between the relative depth (horizontal axis) and the relative dependence
(vertical axis) of the citation impact of highly cited scientometrics publications. The two plots show
different indicators of depth and dependence. P1, P2, P3, and P4 denote four publications selected
for a more detailed analysis.

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Authors

Title

Tableau 6.

The four selected publications and their number of citations and number of references

P1
N. J.. Van Eck & L. Waltman

P2

P3

P4

J.. E. Hirsch

L. Egghe

M.. Thelwall

Software survey: VOSviewer,
a computer program for
bibliometric mapping

An index to quantify an
individual’s scientific
research output

The Hirsch index
and related
impact measures

Extracting macroscopic
information from
Web links

Journal

Scientometrics

Actes du

Annual Review

Journal of the American

National Academy
of Sciences of
the USA

of Information
Science and
Technologie

Society for Information
Science and Technology

Publication year

2009

# cit.

# ref.

# ref. in data

273

37

26

2005

2,518

6

4

2010

116

256

175

2001

107

65

43

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equals 1.19, which indicates that on average a publication citing P1 also cites 1.19 other pub-
lications citing P1. This means that publications citing P1 are only weakly connected by citation
relations. It shows that P1 does not have a very deep citation impact. MR[cited pub] equals 1.07.
Ainsi, when a publication cites P1, on average it also cites 1.07 publications cited by P1.
Chiffre 9 shows that there are a few publications citing P1 that have somewhat more substantial
values for R[citing pub] or R[cited pub]. Unlike most publications citing P1, these may be pub-
lications that contribute to the methodological literature on bibliometric visualization.

Publication P2 is the article by Hirsch (2005) in which he introduced the h-index. This is an
extremely influential publication. With 2,518 citations, P2 is by far the most highly cited scien-
tometrics publication in our data. There are a large number of publications that present studies
of the h-index, propose alternatives to the h-index, or report bibliometric analyses in which the
h-index is applied. In the field of scientometrics, P2 arguably can be seen as the starting point
of a new subfield of research focused on studying bibliometric indicators of the performance of
individual researchers (ou, alternativement, one may suggest there has been an h-bubble; voir
Rousseau, García-Zorita, & Sanz-Casado, 2013). MR[citing pub] equals 5.89 for P2. Ainsi,
on average, publications that cite P2 also cite 5.89 other publications citing P2. This shows that
publications citing P2 are strongly connected by citation relations, which reflects the central
position of P2 in a highly active subfield of research. The dependence of P2 is very low. MR[cited
pub] equals 0.06, indicating that publications citing P2 hardly cite any publications cited by P2.
This suggests that P2 does not only have a central position in a specific subfield of research, mais
that it can be considered a foundational publication in this subfield. Cependant, P2 has only a very
limited number of references (see Table 6), which means that it has a low dependence almost by
necessity. The small number of references of P2 can be seen as additional evidence of the foun-
dational role of this publication, but alternatively it may also be argued to reflect a lack of gen-
erosity in the referencing behavior of the author of P2.

Publication P3 is a review article about the h-index and other related bibliometric indices
(Egghe, 2010). P3 has been cited 116 times in our data. Il a 256 références, of which 175 indiquer
to publications included in our data (see Table 6). The large number of references reflects the
voluminous literature on the h-index published between 2005 et 2010. P3 has a high depen-
dence. MR[cited pub] equals 8.26. Ainsi, when a publication cites P3, on average it also cites

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Chiffre 9. Distributions of R[citing pub] et R[cited pub] for the citing publications of the four selected publications. Dashed vertical lines
indicate the mean of a distribution.

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8.26 publications cited by P3. As can be seen in Figure 9, some publications citing P3 even cite
plus que 20 publications cited by P3. The high dependence of P3 indicates that P3 builds on a
large body of literature and that the citation impact of P3 is strongly dependent on this literature.
This reflects that, as a review article, P3 does not make an original scientific contribution. C'est
sometimes suggested that researchers tend to cite review articles instead of citing the underlying
original works, but the high dependence of P3 shows that this is not the case for P3. MR[citing
pub] equals 1.34. En moyenne, a publication that cites P3 also cites 1.34 other publications citing
P3, indicating that publications citing P3 are only relatively weakly connected by citation rela-
tion. This may be due to the gradual decline in the interest of the scientometric community in
the h-index. It also shows that P3 has not developed into a canonical reference for publications
dealing with the h-index. This may partly be explained by the fact that around 2010 a number of
review articles about the h-index were published more or less at the same time.

Publication P4 is about the extraction of macroscopic information from Web links (Thelwall,
2001). This publication deals with a topic in the field of webometrics, which partly overlaps with
the field of scientometrics. P4 was published in 2001. It has received 107 citations in our data. Comme
can be seen in Figure 8, P4 is a quite unique publication in the scientometric literature, because it
combines a high depth (c'est à dire., MR[citing pub] = 6.75) with a high dependence (c'est à dire., MR[cited pub] =
5.68). This means that publications citing P4 have lots of citation relations both with each other
and with publications cited by P4. As can be seen in Table 6, the number of references of P4 is not
exceptionally large, making the high dependence of P4 even more noteworthy. The high depth of
P4 suggests that P4 makes an important contribution to a relatively narrow but densely connected
area of research. On the other hand, the high dependence of P4 seems to indicate that P4 should
not be regarded as a pioneering publication. The citation impact of P4 is strongly dependent on
earlier publications. Ainsi, P4 can be considered to make an important incremental contribu-
tion, but not a highly innovative one.

8. DISCUSSION AND CONCLUSION

8.1. Résumé

We have proposed a multidimensional framework for characterizing the citation impact of sci-
entific publications. Our framework makes a distinction between the level, the depth and
breadth, and the dependence and independence of the citation impact of a publication. Le
level of citation impact is quantified by the number of citations a publication has received.
The depth and breadth of the citation impact of a publication are operationalized based on
citations from publications citing the focal publication to other publications citing the focal pub-
lication. Inversement, the dependence and independence of the citation impact of a publication
are operationalized based on citations from publications citing the focal publication to publica-
tions cited by the focal publication. Our proposed framework also distinguishes between an
absolute and a relative perspective on the depth and breadth and the dependence and indepen-
dence of citation impact. The absolute perspective scales with the level of citation impact, alors que
the relative perspective normalizes for the level of citation impact.

In a traditional one-dimensional perspective on citation impact, the number of citations
received by a publication is used as an indicator of the impact of the publication on later
publications. Our multidimensional framework offers a more detailed understanding of the
citation impact of a publication. It makes a distinction between publications that have a deep
citation impact, typically in a relatively narrow research area, and publications that have a
broad citation impact, probably covering a wider area of research. It also distinguishes between

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publications that are strongly dependent on earlier work and publications that make a more
independent scientific contribution.

In a case study focusing on the field of scientometrics, we have demonstrated the value of our
proposed framework for characterizing the citation impact of publications. From a relative point
de vue (c'est à dire., after normalizing for the level of citation impact), we found that the article in which
the h-index was introduced has a high depth and a low dependence. This reflects the role of this
article as the starting point of a new subfield of research within the field of scientometrics. On the
other hand, a review article on the h-index has a high dependence, which shows the strong
reliance of this article on earlier works. A high dependence can be expected to be a typical feature
of review articles. The article in which the VOSviewer software was introduced has a low depth,
reflecting that it has a broad rather than a deep citation impact. Enfin, an article in the field of
webometrics has a high depth and a high dependence, indicating that this article contributes to a
strongly cumulative research area, but that it does not play a pioneering role in this area.

8.2. Applications

The ideas introduced in this paper may have all kinds of applications, for instance in research
assessment and scientific literature search.

In the context of research assessment, our proposed multidimensional citation impact frame-
work offers new information for evaluating publications. Two publications that have received a
similar number of citations may have quite different characteristics in terms of the depth and
breadth and the dependence and independence of their citation impact. This information
may be provided to research evaluators in a process of peer review. Par exemple, when evalu-
ators assess the publication output of a researcher, the information may help draw the evalua-
tors’ attention to publications with special characteristics, such as a very broad or a very deep
citation impact. Evaluators may then choose to study these publications in more detail.

In the context of scientific literature search, our proposed framework may facilitate alternative
ways of presenting search results. In many literature search systems, publications can be ranked
based on their number of citations. Indicators of absolute depth and breadth and absolute
dependence and independence may be used as alternative criteria for ranking publications.
Another possibility is to use these indicators to assign badges to publications, for instance to
highlight publications that have an exceptionally broad or an exceptionally deep citation
impact. In this way, these publications can be given special emphasis in the presentation of
search results.

We acknowledge that the above applications of the ideas presented in this paper require
additional research. For specific applications, some of our proposed indicators may turn out
to be more useful than others. The indicators may also require additional fine-tuning to optimize
them for a specific use case.

8.3. Future Research

There are many directions for future research. First of all, additional case studies can be carried
out to assess the usefulness and validity of our proposed multidimensional citation impact
framework. Such case studies could also analyze how the proposed indicators change over time
for individual publications, and how such changes relate to the accumulation of citations for a
given focal publication. Aussi, the proposed framework can be extended in various ways, pour
instance by taking into account publication type (par exemple., review articles), citation type (par exemple.,
self-citations), and citation context (par exemple., location in the full text of the citing publication). Pour

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instance, if we omit self-citations, how does this affect the values of the indicators? And how do
the values of the indicators differ between review articles and regular articles?

Ideas similar to the ones proposed in this paper can also be explored at aggregate levels rather
than at the level of individual publications. Par exemple, based on the current framework, indi-
cators of depth can be defined at the level of authors instead of publications. One approach
could be to first determine the depth of each publication of an author and to then aggregate
the outcomes from the publication level to the author level. Another approach could be to
consider an author-author citation network and to determine the depth of an author based on
this network.

Enfin, the distinction between cumulative research and more independent research can be
studied in alternative ways. Research areas that are of a strongly cumulative nature, par exemple,
may be identified by searching for densely connected subnetworks in a citation network.

REMERCIEMENTS

We are grateful to Lutz Bornmann and to anonymous reviewers for their helpful comments on
our work. Yi Bu also would like to thank Ying Ding, Yong-Yeol Ahn, Johan Bollen, Staša
Milojevic(cid:1), Cassidy R. Sugimoto, Dashun Wang, Xianlei Dong, and Jian Xu for their feedback.
An earlier version of this paper was presented at the 17th International Conference on
Scientometrics and Informetrics (ISSI 2019).

CONTRIBUTIONS DES AUTEURS

Yi Bu: Conceptualisation, Conservation des données, Analyse formelle, Enquête, Méthodologie, Project
administration, Validation, Visualisation, Writing—original draft, Writing—review & édition. Ludo
Waltman: Conceptualisation, Enquête, Méthodologie, Gestion de projet, Surveillance,
Validation, Writing—review & édition. Yong Huang: Enquête, Validation, Visualisation.

COMPETING INTERESTS

Ludo Waltman is Editor-in-Chief of Quantitative Science Studies. The peer review process for
this paper was handled by Vincent Larivière, Associate Editor of the journal. The authors have no
other competing interests.

INFORMATIONS SUR LE FINANCEMENT

Yi Bu acknowledges financial support from the National Natural Science Foundation of China
(Non. 71904081) and the Chinese Education Department Research Foundation for Humanities
and Social Sciences (Non. 19YJC870017).

DATA AVAILABILITY

The data used in this paper was obtained from the WoS database. We are not allowed to
redistribute the data. Cependant, a subset of the data used in Section 7 is available in Zenodo
(Bu & Waltman, 2020).

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Études scientifiques quantitatives

177

je

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A multidimensional framework for characterizing the citation impact of scientific publications

APPENDIX

Table A1.

Spearman’s rank correlation coefficients for indicators of the depth and breadth of the citation impact of publications (all disciplines).

CP(R.[citing pub] = 0)

CP(R.[citing pub] > 0)

PCP(R.[citing pub] = 0)

PCP(R.[citing pub] > 0)

TR[citing pub]

MR[citing pub]

CP
(R.[citing pub] = 0)
1.00

CP
(R.[citing pub] > 0)
0.07

PCP
(R.[citing pub] = 0)
0.69

PCP
(R.[citing pub] > 0)
−0.69

TR
[citing pub]
−0.22

MR
[citing pub]
−0.62

0.07

0.69

−0.69

−0.22

−0.62

1.00

−0.61

0.61

0.90

0.60

−0.61

1.00

−1.00

−0.81

−0.94

0.61

−1.00

1.00

0.81

0.94

0.90

−0.81

0.81

1.00

0.86

0.60

−0.94

0.94

0.86

1.00

je

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3

Table A2.
(all disciplines).

Spearman’s rank correlation coefficients for indicators of the dependence and independence of the citation impact of publications

CP(R.[cited pub] = 0)

CP(R.[cited pub] > 0)

PCP(R.[cited pub] = 0)

PCP(R.[cited pub] > 0)

TR[cited pub]

MR[cited pub]

CP
(R.[cited pub] = 0)
1.00

CP
(R.[cited pub] > 0)
0.04

PCP
(R.[cited pub] = 0)
0.84

PCP
(R.[cited pub] > 0)
−0.84

TR
[cited pub]
−0.26

MR
[cited pub]
−0.73

0.04

0.84

−0.84

−0.26

−0.73

1.00

−0.46

0.46

0.84

0.41

−0.46

1.00

−1.00

−0.67

−0.87

0.46

−1.00

1.00

0.67

0.87

0.84

−0.67

0.67

1.00

0.78

0.41

−0.87

0.87

0.78

1.00

Études scientifiques quantitatives

178

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Table A3.
(c'est à dire., absolute breadth), CP(R.[cited pub] > 0) (c'est à dire., absolute dependence), and CP(R.[cited pub] = 0) (c'est à dire., absolute independence).

Top 10 scientometrics publications ranked by five citation impact indicators: CP (c'est à dire., level), CP(R.[citing pub] > 0) (c'est à dire., absolute depth), CP(R.[citing pub] = 0)

Ranked by CP

CP
(R.[citing
pub] > 0)

CP
(R.[citing
pub] = 0)

CP
(R.[cited
pub] > 0)

CP
(R.[cited
pub] = 0)

CP

Title

Journal

First author

2519

2086

433

118

2401

An index to quantify an individual’s

Actes de la Nationale

HIRSCH, JE

scientific research output

Academy of Sciences of the
United States of America

Year

2005

659

450

209

207

452

The increasing dominance of teams

Science

WUCHTY, S

2007

582

481

462

483

279

262

99

202

200

450

224

226

400

188

212

535

110

292

17

21

371

170

433

in production of knowledge

47

Theory and practise of the g-index

Scientometrics

The scientific impact of nations

Nature

EGGHE, L

KING, DA

2006

2004

Coauthorship networks and patterns

Actes de la Nationale

NEWMAN, MEJ

2004

of scientific collaboration

Academy of Sciences of the
United States of America

Comparison of PubMed, Scopus,
Web de la Science, and Google
Scholar: Strengths and weaknesses

FASEB Journal

FALAGAS, ME

2008

379

A guide for naming research studies

International Journal of Clinical

MONTERO, je

2007

in Psychology

and Health Psychology

397

214

183

197

200

Science faculty’s subtle gender biases

Actes de la Nationale

MOSS-RACUSIN,

2012

favor male students

Academy of Sciences of the
United States of America

Californie

375

267

108

242

133

The impact of research collaboration

Social Studies of Science

LEE, S

2005

355

245

110

229

126

Impact of data sources on citation

on scientific productivity

counts and rankings of LIS faculty:
Web of Science versus Scopus
and Google Scholar

1
7
9

Journal of the American Society
for Information Science and
Technologie

MEHO, LI

2007

UN
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d
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s
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un
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F
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F
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:
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Table A3.

(a continué ).

Ranked by CP(R.[citing pub] > 0)

CP
(R.[citing
pub] > 0)

CP
(R.[citing
pub] = 0)

CP
(R.[cited
pub] > 0)

CP
(R.[cited
pub] = 0)

CP

Title

Journal

First author

2519

2086

433

118

2401

An index to quantify an individual’s

Actes de la Nationale

HIRSCH, JE

scientific research output

Academy of Sciences of the
United States of America

582

659

481

375

483

450

279

267

99

209

202

108

535

207

110

242

47

Theory and practise of the g-index

Scientometrics

452

The increasing dominance of teams

Science

in production of knowledge

EGGHE, L

WUCHTY, S

371

133

The scientific impact of nations

Nature

KING, DA

The impact of research collaboration

Social Studies of Science

LEE, S

on scientific productivity

Year

2005

2006

2007

2004

2005

462

262

200

292

170

Coauthorship networks and patterns

Actes de la Nationale

NEWMAN, MEJ

2004

of scientific collaboration

355

245

110

229

126

Impact of data sources on citation

counts and rankings of LIS faculty:
Web of Science versus Scopus
and Google Scholar

Academy of Sciences of the
United States of America

Journal of the American Society
for Information Science and
Technologie

MEHO, LI

2007

327

240

87

287

40

Does the h-index have predictive

Actes de la Nationale

HIRSCH, JE

2007

pouvoir?

Academy of Sciences of the
United States of America

286

234

52

249

37

450

224

226

17

433

1
8
0

Comparison of the Hirsch-index
with standard bibliometric
indicators and with peer judgment
pour 147 chemistry research groups

Comparison of PubMed, Scopus,
Web de la Science, and Google
Scholar: Strengths and weaknesses

Scientometrics

VAN RAAN, AFJ

2006

FASEB Journal

FALAGAS, ME

2008

UN
m
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r
2
0
2
3

Ranked by CP(R.[citing pub] = 0)

CP
(R.[citing
pub] > 0)

CP
(R.[citing
pub] = 0)

CP
(R.[cited
pub] > 0)

CP
(R.[cited
pub] = 0)

CP

Title

Journal

First author

2519

2086

433

118

2401

An index to quantify an individual’s

Actes de la Nationale

HIRSCH, JE

scientific research output

Academy of Sciences of the
United States of America

Year

2005

450

224

226

400

188

212

17

21

433

Comparison of PubMed, Scopus,
Web de la Science, and Google
Scholar: Strengths and weaknesses

FASEB Journal

FALAGAS, ME

2008

379

A guide for naming research studies

International Journal of Clinical

MONTERO, je

2007

in Psychology

and Health Psychology

659

450

209

207

452

The increasing dominance of teams

Science

WUCHTY, S

2007

in production of knowledge

481

462

253

397

279

262

69

214

202

200

184

183

110

292

0

197

371

170

253

200

The scientific impact of nations

Nature

KING, DA

2004

Coauthorship networks and patterns

Actes de la Nationale

NEWMAN, MEJ

2004

of scientific collaboration

Academy of Sciences of the
United States of America

Who’s afraid of peer review?

Science

BOHANNON, J.

2013

Science faculty’s subtle gender
biases favor male students

Actes de la Nationale

MOSS-RACUSIN,

2012

Academy of Sciences of the
United States of America

Californie

186

39

147

33

153

The rate of growth in scientific

Scientometrics

LARSEN, PO

2010

345

200

145

189

156

publication and the decline in
coverage provided by Science
Index des citations

What do citation counts measure?
A review of studies on citing
behavior

Journal of Documentation

BORNMANN, L

2008

UN
m
toi
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s
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F
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F
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1
8
1

je

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F
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:
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6
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Q
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v
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c
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S
toi
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t

je

Table A3.

(a continué ).

Ranked by CP(R.[cited pub] > 0)

CP
(R.[citing
pub] > 0)

CP
(R.[citing
pub] = 0)

CP
(R.[cited
pub] > 0)

CP
(R.[cited
pub] = 0)

Title

Journal

First author

CP

582

462

483

262

99

200

535

292

47

Theory and practise of the g-index

Scientometrics

EGGHE, L

170

Coauthorship networks and patterns

Actes de la Nationale

NEWMAN, MEJ

2004

of scientific collaboration

Academy of Sciences of the
United States of America

Year

2006

327

240

87

287

40

Does the h-index have predictive

Actes de la Nationale

HIRSCH, JE

2007

pouvoir?

Academy of Sciences of the
United States of America

286

234

52

249

37

Comparison of the Hirsch-index
with standard bibliometric
indicators and with peer judgment
pour 147 chemistry research groups

Scientometrics

VAN RAAN, AFJ

2006

375

267

108

242

133

The impact of research collaboration

Social Studies of Science

LEE, S

on scientific productivity

241

204

37

236

5

The R- and AR-indices:

Chinese Science Bulletin

JIN, BH

Complementing the h-index

2005

2007

355

245

110

229

126

Impact of data sources on citation

276

209

67

223

53

counts and rankings of LIS faculty:
Web of Science versus Scopus and
Google Scholar

Universality of citation distributions:
Toward an objective measure of
scientific impact

Journal of the American Society
for Information Science and
Technologie

MEHO, LI

2007

Actes de la Nationale

RADICCHI, F

2008

Academy of Sciences of the
United States of America

659

450

209

207

452

The increasing dominance of teams

Science

WUCHTY, S

2007

222

188

34

206

16

1
8
2

in production of knowledge

Is it possible to compare researchers
with different scientific interests?

Scientometrics

BATISTA, PD

2006

UN
m
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d
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s
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un
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F
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F
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2
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q
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9
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7
S
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m
b
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r
2
0
2
3

Ranked by CP(R.[cited pub] = 0)

CP
(R.[citing
pub] > 0)

CP
(R.[citing
pub] = 0)

CP
(R.[cited
pub] > 0)

CP
(R.[cited
pub] = 0)

CP

Title

Journal

First author

2519

2086

433

118

2401

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