[1,2]

Collected the data and performed the analysis; Prepared figures and wrote the
manuscript

[orcid=0000-0002-3797-7363] Designed and performed the analysis; Prepared
figures and wrote the manuscript

[cor1]Corresponding author

# Impact of $h$-index on authors ranking: An improvement to the $h$-index for
lower-ranked authors

Parul Khurana  Kiran Sharma<EMAIL_ADDRESS>School of Computer
Applications, Lovely Professional University, Phagwara, Punjab-144401, India
School of Engineering and Technology, BML Munjal University, Gurugram,
Haryana-122413, India

###### Abstract

In academia, the research performance of a faculty is either evaluated by the
number of publications or the number of citations. Most of the time $h$-index
is widely used during the hiring process or the faculty performance
evaluation. The calculation of the $h$-index is shown in various databases;
however, there is no systematic evidence about the differences between them.
Here we analyze the publication records of 385 authors from Monash University
(Australia) to investigate (i) the impact of different databases like Scopus
and WoS on the ranking of authors within a discipline, and (ii) to complement
the $h$-index, named $h_{c}$, by adding the weight of the highest cited paper
to the $h$-index of the authors. The results show the positive impact of
$h_{c}$ on the lower-ranked authors in every discipline. Also, Scopus provides
overall better ranking than WoS; however, for disciplines, the ranking varies
among Scopus and WoS.

###### keywords:

$h$-index $g$-index $h_{c}$-index Authors ranking

To check the impact of $h$-index on authors ranking within a university based
on Scopus and WoS.

The introduction of $h_{c}$ which is a complement to $h$-index, takes into
account the weight of the highest cited paper.

Giving weight to highest cited paper significantly improves the performance of
the lower-ranked authors, especially for $h\leq 10$. For higher rank,
$h_{c}==h$ and for lower rank, $h_{c}\geq h$.

The performance of Scopus and WoS varies among disciplines, hence the ranking
varies.

##  1 Introduction

Scientific evaluation is best carried out with the number of publications, the
number of citations, and contribution of an author to scientific knowledge and
society (Martin, 1996; Garfield, 2006). However, citation analysis plays a
crucial role while evaluating the research performance of an individual in the
academic community, that is why it acts as a key tool in scientometrics
(Cronin et al., 1997; Bornmann and Daniel, 2005; Molinari and Molinari, 2008;
Bornmann, 2017). Along with the citations, the number of publications and
$h$-index also have a strong stand in research evaluation (Hirsch, 2005). To
perform the fair evaluation of an individual within a university/institution,
funding bodies, scientific society, etc., it is the essential requirement that
the considered scientometric parameters should be field, discipline, and time
normalized (Waltman, 2016). However, with the rapid increase in the number of
scholarly databases or libraries like Google Scholar, Scopus, Web of Science,
Dimension, PubMed, etc., the choice of database consideration has become
tedious due to the choice of considered journals (Bakkalbasi et al., 2006;
Falagas et al., 2008; Meho and Yang, 2007; Mongeon and Paul-Hus, 2016; Martín-
Martín et al., 2018).

As proposed by Hirsch (2005) “A scientist has index $h$ if $h$ of his/her
$N_{p}$ papers have at least $h$ citations each and the other ($N_{p}-h$)
papers have $\leq h$ citations each.” In bibliometric, $h$-index is considered
as one of the important, robust, primitive, quantified, and a single measure
used to evaluate the individual’s work quality, impact, influence, and
importance (Bar-Ilan et al., 2007; Bar-Ilan, 2008). However, the popularity
and the interest gained by the $h$-index is due to its simple calculation
among the scientific community (Ball, 2005; Dumé, 2005; Glänzel, 2006).
Instead of presenting individual values like the number of publications, and
the number of citations, etc. which are giving a single dimension of the
author’s performance, $h$-index introduced multidimensional presentation
(quantity and impact) and that is too with a single integer number (Maabreh
and Alsmadi, 2012). Hence, it is considered as a balanced way to combine and
evaluate the broad scientific impact of an author (Braun et al., 2005). Gracza
et al. have suggested $h$-index of an author as equivalent to the impact
factor of a journal (Gracza and Somoskövi, 2007). Braun et al. have identified
$h$-index as a measure of journal credibility and assessments as well (Braun
et al., 2006). Due to its popularity, different indexing databases like
Scopus, WoS, etc. provides the calculated $h$-index of an author on their
website (Egghe, 2008; Abramo et al., 2010).

Over the numerous advantages, it has some drawbacks too as mentioned by Hirsch
in his core publication (Hirsch, 2005; Costas and Bordons, 2007). To overcome
such limitations, many new indices were proposed in this line and one such
index is $g$-index (Egghe, 2006b; Batista et al., 2006; Costas and Bordons,
2007; Vinkler, 2007; Bornmann et al., 2008; Schreiber, 2008a; Costas and
Bordons, 2008). The limitations of not considering highly cited papers, have
encouraged Leo Egghe to propose $g$-index in 2006 as follows: “A set of papers
has a g-index g if g is the highest rank such that the top $g$ papers have,
together, at least $g^{2}$ citations. This also means that the top $g+1$
papers have less than $(g+1)^{2}$ papers” (Egghe, 2006a). In comparison, the
$g$-index shows improvement to $h$-index by giving more credit to highly cited
papers and more discriminatory power to represent the scientific impact of
author (Schreiber, 2008b; Tol, 2008). Further, Leo Egghe introduced the
concept of adding fictitious articles with 0 citations to overcome the
limitations and complete the calculation of $g$-index (Egghe, 2006b).

Over time, researchers have shown the use and importance of the $h$-index
while calculating the ranking of authors, universities, the impact of a
journal, etc. (Bornmann and Daniel, 2009; Torres-Salinas et al., 2009; Vieira
and Gomes, 2009). Dunaiski et al. have evaluated the bias and performance of
the authors over a range of citations; however, no significant differences
between the globalized and averaged variants based on citations were found
(Dunaiski et al., 2019). Different approaches have been used in literature to
analyze the author’s ranking. Authors have also shown the use of page rank
algorithm on the author co-citations network to get the respective ranking
(Ding et al., 2009; Nykl et al., 2015; Dunaiski et al., 2016, 2018). Usman et
al. have shown in their research the analysis of various assessment parameters
like $h$-index, citations, publications, authors per paper, $g$-index, hg-
index (Alonso et al., 2010), R-index (Jin et al., 2007), e-index (Zhang,
2009a), h’-index (Zhang, 2013), w-index (Zhang, 2009b) etc. to evaluate the
authors ranking (Usman et al., 2020).

$h$-index ignores the highly cited papers that means it under-estimates the
academic performance of the scientists. On the other hand, the $g$-index takes
care of highly cited papers; however, it reduces the impact of the highest
cited paper significantly (Ding et al., 2020). The present study resolves this
problem by introducing a complementary index, named $h_{c}$, that is
complimenting $h$-index by including the weight of the highest cited paper
while keeping the most important advantage of the $h$-index (a single-number
to measure the academic performance). In general, the aim of the study is to
highlight the impact of the $h$-index on the author’s ranking while measuring
their performance within an institution. Here we have examined the research
contribution of an individual of Monash University in terms of the $h$-index
and the weight of the highest cited paper from Scopus and WoS. This study aims
to investigate the following points:

  1. 1.

Impact of $h$-index on authors ranking based on different databases like
Scopus and WoS.

  2. 2.

Improving $h$-index by considering the weight of the highest cited paper that
in turn improves the performance of the lower-ranked authors.

The study is organized as follows: Section 2 is on data description including
data selection, data filtration, and discipline-wise publications analysis.
Results are explained in Section 3. Finally, the discussion and conclusion is
presented in Section 4.

##  2 Data description

###  2.1 Data selection

Figure 1: (left panel) Flowchart describing the process of visiting the
author’s profile.(right panel) Data extraction and filtration from Scopus and
WoS.

Data selection has two important aspects, first, what research question are we
going to answer? and second, what is the required approach to answering the
question? The goal is to study the ranking of authors based on the number of
publications, citations, and $h$-index computed from Scopus and WoS. The
choice of the databases is arbitrary and is on the availability of the data.
The very first challenge is the selection of the authors. On what basis an
author should be selected is a major concern. To get detailed information
about the scholarly data of any author we need authentic information. Indexing
databases like Scopus or WoS track the author identity information with Author
ID or Researcher ID or Orcid ID. There are two ways to approach this: one is
to look for any open-source dataset like Kaggle, etc. and the other is to look
manually at the university websites. Finally, we have found that Monash
University, a public research university in Australia has provided the
profiles of 6316 persons associated with the university at different
designations and in different disciplines. There are three associated benefits
with this dataset:

  * •

First, all the profiles are sorted on the basis of the last name of persons.

  * •

Second, authors Orcid, Researcher, and Scopus IDs are mentioned.

  * •

Third, a search tab is given on the website to filter the profiles with at
least 5 years or 10 years’ work with the university.

Then, we started searching the profiles of persons manually by opening all the
profiles one by one. A further requirement of the research question is to
identify those profiles which have all of three IDs: Orcid ID, Researcher ID,
and Author ID. Orcid ID is a digital identifier and is used to uniquely
identify authors across different platforms. Researcher ID is a digital
identifier used by WoS to maintain the database of authors. Author ID is used
by Scopus for the unique identification of authors. After checking each and
every profile manually on the website of Monash University, we have considered
the profile carrying all three IDs (see flowchart in Figure 1 (left panel)).
To critically evaluate the identified research question, we have recorded the
discipline of persons along with all three IDs (Orcid, Researcher, and
Author). In the end, a sample of 385 persons from various disciplines is
finalized and used to analyze the identified research questions.

###  2.2 Data filtration

In order to perform the analysis, we have visited the profiles of 385 authors
listed on the Monash University website
https://research.monash.edu/en/persons/, which is freely available. Extracting
different IDs (Orcid, Researcher, and Author) to avoid author ambiguity at any
stage, later on, is the initial step of scrapping the data. So, the
information extracted from Monash University regarding 385 authors is (see
Fig. 1 (left panel)):

  * •

Author name

  * •

Authors Orcid, Researcher, and Scopus ID

  * •

Authors disciplines or subject categories

Further, we have extracted the following information from both Scopus and WoS
using respective API’s (see Fig. 1 (right panel):

  * •

Author name, affiliation, $h$-index

  * •

Detailed records of the number of publications and citations received on those
publications for all 385 authors

  * •

Doi’s of all publications

A total of 31267 documents are downloaded for all authors from Scopus and
30138 from WoS. To maintain the uniqueness among downloaded data, we have
considered all the records with doi numbers only. Thus, we have filtered the
number of documents in Scopus with doi as 28833 (92.2%) and 24975 (82.9%) in
WoS. Further, we have filtered the common (both in Scopus and WoS) and unique
(either Scopus or WoS) documents across both indexing databases. We have found
that Scopus has 5664 (19.6%) unique documents, and WoS has 1806 (7.2%) unique
documents. 23169 (80.4% Scopus, 92.8% WoS) of documents are common in both
indexing databases.

We have categorized 385 records into five disciplines: Biochemistry and
Molecular Biology, Engineering, Health and Medical Sciences, Natural Sciences,
and Social Sciences. In broader sense, Biochemistry and Molecular Biology
includes microbiology, blood diseases, molecular sciences, etc. Engineering
includes civil, computer, electrical, mechanical, etc. Health and Medical
Sciences includes epidemiology, medicine, physiology, etc. Natural Sciences
includes physics, chemistry, mathematics, etc. Social Sciences includes
sociology, economics, psychology, etc.

Table 1: A total number of authors, total publications along with unique and common publications, total citations, and publications received citations of five disciplines for both indexing databases (ID): Scopus (S) and WoS (W). Disciplines |  | Total
---
Authors
ID |  | Total
---
Pubs
| Unique
---
Pubs
| Pubs
---
Received
Citations
| Total
---
Citations
| Common
---
Pubs
Biochemistry and Molecular Biology | 88 | S | 7095 | 972 | 6553 | 294374 | 5732
W | 6979 | 366 | 6241 | 283221
Engineering | 60 | S | 5746 | 1221 | 4899 | 137875 | 3806
W | 5212 | 270 | 4418 | 124490
Health and Medical Sciences | 106 | S | 9687 | 1786 | 8503 | 352286 | 7125
W | 9807 | 724 | 7813 | 330846
Natural Sciences | 46 | S | 3266 | 500 | 2964 | 101380 | 2577
W | 3055 | 123 | 2773 | 96889
Social Sciences | 85 | S | 5473 | 1185 | 4762 | 164524 | 3929
W | 5085 | 323 | 4122 | 141739

###  2.3 Discipline-wise publications analysis

Figure 2: (a) Discipline-wise proportion of the number of publications (common
and unique) in Scopus and WoS. Unique publications are those which only appear
either in Scopus (S) or in WoS (W). Common publications are the intersection
of Scopus and WoS publications. (b) Number of publications received citations
for Scopus and WoS.

Figure 2 (a) shows the proportion of number of common and unique publications
in Scopus and WoS. Biochemistry and Molecular Biology and Natural Sciences
contains more than 80% of common publications whereas Engineering, Health and
Medical Sciences, and Social Sciences contains more than 70% of common
publications. Similarly, Engineering and Social Sciences contains more than
20% of the unique Scopus publications, whereas WoS contains less than 10% of
unique publications. On average, the number of common publications is 76%,
unique-Scopus is 19%, and Unique-WoS is 5%. Hence, the number of unique-Scopus
publications is higher in all disciplines as compared to unique-WoS (Falagas
et al., 2008; Mongeon and Paul-Hus, 2016).

Figure 2 (b) shows the proportion of publications that received citations from
both Scopus and WoS. In Natural Sciences both Socpus and WoS contains more
than 90% of publications that received citations. However, in Biochemistry and
Molecular Biology Scopus contains more than 90% publications. In Scopus,
Engineering, Health and Medical Sciences, and Social Sciences contains more
documents that received citations as compared to WoS. An index is being
calculated on the number of publications and citations received on those
publications. The variation in the number of publications in any database like
Scopus, WoS, Google Scholar, MAG, PubMed, etc. affects the index computed on
those publications (Meho and Yang, 2007; Martín-Martín et al., 2018). We will
see this variation further in the study. For the detail count of the number of
authors, publications, unique publications, the number of publications that
received citations, total citations, and common publications for both Scopus
and WoS for five disciplines see Table 1.

##  3 Results

###  3.1 Authors ranking based on $h$, $g$, and $h_{c}$

Figure 3 shows the ranking of authors for five disciplines in terms of $h$\-
and $g$\- indices. The ranks are sorted according to Scopus $h$-index and
$g$-index is being plotted for authors respectively. A large number of
fluctuation is observed for the authors with varying $h$-index in all
disciplines. In Biochemistry and Molecular Biology, Health and Medical
Sciences, and Social Sciences, the minimum value of $g$ is nearly double of
$h$ in Scopus; whereas in WoS it is observed only in Biochemistry and
Molecular Biology. Also, the average index value of $g$ is close to double of
$h$ for all disciplines.

(a) (f) (b) (g) (c) (h) (d) (i) (e) (j)

Figure 3: Ranking of 385 authors based on the $h$ and $g$ for both Scopus and
WoS for five disciplines. The ranks are sorted according to the $h$-index of
Scopus.

(a) (f) (b) (g) (c) (h) (d) (i) (e) (j)

Figure 4: Ranking of 385 authors based on the $h$ and $h_{c}$ for both Scopus
and WoS for five disciplines. The ranks are sorted in descending order
according to the $h$-index of Scopus. Inset: shows the probability density
function for both $h$ and $h_{c}$.

####  3.1.1 Definition of the $h_{c}$

In this work, we have proposed a complementary analysis to the existing
$h$-index, named $h_{c}$. Here, we are providing weight to the highest cited
paper and add it to the $h$-index of an author. To get the weight of the
highest cited paper, check the following condition

$h^{k}<H_{cite},$ (1)

where $1<h<H_{cite}$. $H_{cite}$ is the count of highest cited paper of an
author and $k$ is the weight of the highest cited paper and $k\geq 2$. Now
$h_{c}$ is computed as

$h_{c}=h+k.$ (2)

Here, $h_{c}\geq h$.For $k=1$ the condition 1 will always be True and it will
not add any value to the ranking. Hence, we reject the case.

####  3.1.2 Comparative analysis of $h$ and $h_{c}$

Table 2 explains the three case studies representing different scenarios of
the research productivity. $P_{n}$ represents the paper number, CR is
citations received, $k$ is the calculated weight of the highest cited paper
$H_{cite}$.

$i=2,k=0$

while  _$h^{i} <H_{cite}$_ do

$k=i$

$i=i+1$

end while

$h_{c}=h+k$

Algorithm 1 Calculation of $h_{c}$

  * •

Case I: Here, $h=4$ as 4 of the papers are having citations greater than or
equal to 4 each. $H_{cite}=15$ for 10 publications (first paper of $P_{n}$ as
papers are sorted in descending order according to citations received). From
algorithm 1, we get $k=0$, hence, $h_{c}=h=4$. So, no change is observed.

Case II: Here, $h=5$ and $H_{cite}=65$. From algorithm 1, we get $k=2$, hence,
$h_{c}=7$. So , it has raised the index value by 2.

Case III: Here, $h=5$ and $H_{cite}=205$. From algorithm 1, we get $k=3$,
hence, $h_{c}=8$. So , it has raised the index value by 3.

Figure 4 shows the changes in $h_{c}$ with respect to $h$ for both Scopus and
WoS. The inset shows probability density function of $h$ and $h_{c}$. The
minor shift of the $h_{c}$ towards the right shows the impact of $h_{c}$ on
lower-ranked authors. The major impact is on Social Sciences where the index
value of 32.9% persons in Scopus and 37.6% in WoS has been increased by $k=2$.
Similarly, for $k=3$, 2.4% in Scopus and 5.9% in WoS has been increased. The
second highest is Health and Medical Sciences with 31% in Scopus and 26.4% in
WoS for $k=2$. There is negligible impact for $k=3$. In Biochemistry and
Molecular Biology, 22.7% in Scopus and 23.9% in WoS for $k=2$ and for $k=3$
the impact is negligible. In Engineering, 16.7% in Scopus and 15% in WoS for
$k=2$ and for $k=3$ it is 5% for both Scopus and WoS. In Natural Sciences,
19.6% in Scopus and 21.7% in WoS for $k=2$ and for $k=3$ it is 2.2% only for
WoS. The overall impact is 24.6% in Scopus and 24.9% in WoS for $k=2$ and 2.1%
in Scopus and 3% in WoS for $k=2$. The overall impact is almost same among
Scopus and WoS; however, variations are visible in disciplines. In Health and
Medical Sciences WoS provides stable ranking whereas in Natural Sciences and
Social Sciences Scopus provides stable ranking. In Biochemistry and Molecular
Biology, and Engineering the difference is negligible. In all disciplines, the
minimum index value has been either increased, or remained same, i.e.
$h_{c}\geq h$ as shown in Table 3. In some cases, $h_{c}$ is showing gain in
minimum index value as compare to $g$. There is no change in the maximum index
value, i.e. $h==h_{c}$ and a slight deviation in median values for both Scopus
and WoS. The average index value is almost same among Scopus and WoS for all
disciplines.

Table 2: Demonstration of $h$ and $h_{c}$. Case I |  | Case II |  | Case III
---|---|---|---|---
h | $h_{c}$ |  | h | $h_{c}$ |  | h | $h_{c}$
| $P_{n}$
---
CR | $k$ | $h^{k}$ |  | $h^{k}<H_{cite}$
---
|  | $P_{n}$
---
CR | $k$ | $h^{k}$ |  | $h^{k}<H_{cite}$
---
|  | $P_{n}$
---
CR | $k$ | $h^{k}$ |  | $h^{k}<H_{cite}$
---
1 | 15 | 2 | 16 | F |  | 1 | 65 | 2 | 25 | T |  | 1 | 205 | 2 | 25 | T
2 | 13 |  |  | 2 | 9 | 3 | 125 | F |  | 2 | 150 | 3 | 125 | T
3 | 10 |  $h_{c}$ = $h+k$ $h_{c}$ = 4+0 $h_{c}$ = 4 |  | 3 | 8 |  $h_{c}$ = $h+k$ $h_{c}$ = 5+2 $h_{c}$ = 7 |  | 3 | 85 | 4 | 625 | F
4 | 7 |  | 4 | 7 | 4 | 40 |  $h_{c}$ = $h+k$ $h_{c}$ = 5+3 $h_{c}$ = 8
5 | 3 |  | 5 | 5 | 5 | 25
6 | 2 |  | 6 | 5 | 6 | 5
7 | 1 |  | 7 | 2 | 7 | 4
8 | 1 |  | 8 | 2 | 8 | 4
9 | 1 |  | 9 | 1 | 9 | 2
10 | 0 |  | 10 | 0 | 10 | 1
|  $h$ = 4
---
$H_{cite}$ = 15
|  |  $h$ = 5
---
$H_{cite}$ = 65
|  $h$ = 5
---
$H_{cite}$ = 205
Table 3: Statistics of $h$, $h_{c}$ and $g$ in terms of min, max, median, average, and standard deviation (SD) of both indexing databases (ID) Scopus and WoS for all five disciplines. Disciplines | ID | Min | Max | Median | Average | SD
---|---|---|---|---|---|---
h | $h_{c}$ | g | h | $h_{c}$ | g | h | $h_{c}$ | g | h | $h_{c}$ | g | h | $h_{c}$ | g
Biochemistry and Molecular Biology | S | 4 | 7 | 11 | 79 | 79 | 137 | 22 | 23 | 43 | 25.2 | 25.6 | 47.5 | 15.3 | 15.1 | 27.1
W | 5 | 6 | 10 | 77 | 77 | 133 | 22 | 22 | 41 | 24.5 | 25.0 | 46.2 | 15.0 | 14.8 | 27.3
Engineering | S | 2 | 5 | 3 | 64 | 64 | 102 | 18 | 18 | 31 | 20.7 | 21.2 | 36.2 | 14.0 | 13.5 | 23.0
W | 1 | 1 | 2 | 62 | 62 | 99 | 16 | 18 | 30 | 19.6 | 20.0 | 34.4 | 13.5 | 13.2 | 22.8
Health and Medical Sciences | S | 2 | 4 | 4 | 91 | 91 | 173 | 17 | 17 | 33 | 21.6 | 22.3 | 41.9 | 16.1 | 15.8 | 33.9
W | 2 | 4 | 3 | 95 | 95 | 168 | 16 | 16 | 30 | 20.6 | 21.2 | 39.6 | 16.1 | 15.9 | 33.9
Natural Sciences | S | 4 | 4 | 6 | 50 | 50 | 98 | 18 | 19 | 36 | 21.2 | 21.6 | 38.1 | 12.2 | 11.9 | 22.1
W | 2 | 5 | 4 | 49 | 49 | 101 | 17 | 18 | 33 | 20.6 | 21.1 | 36.8 | 12.3 | 11.9 | 22.0
Social Sciences | S | 1 | 1 | 2 | 72 | 72 | 146 | 13 | 14 | 25 | 17.0 | 17.7 | 31.6 | 13.9 | 13.6 | 26.7
W | 1 | 1 | 1 | 68 | 68 | 141 | 11 | 13 | 23 | 15.4 | 16.3 | 28.8 | 13.2 | 12.9 | 24.9

###  3.2 Impact of indexing databases on authors ranking

Figure 5 shows the distribution of 385 authors among five disciplines with
varying $h$-index for (a) Scopus and (b) WoS. We have placed the authors into
six categories with varying $h$-index. In total 23.4% of authors are having
$h\leq 10$ in Scopus and 28.6% in WoS. However, after complementing $h$ index
as $h_{c}$, this proportion lower down as 19.7% for Scopus and 24.9% for WoS
for $h_{c}\leq 10$. On the other hand, Scopus has 34.5% and WoS has 32.2% of
authors in the range $11\geq h\leq 20$, whereas this count has increased for
$h_{c}$ as 36.6% for Scopus and 34.8% for WoS. Hence, there is a 2% gain in
the authors count for both Scopus and WoS. For higher-ranked authors ($h>50$
), Scopus has 4.4% and WoS has 4.2% of authors, and $h_{c}$ shows no impact on
authors ranking at a higher level. Table 4 shows the distribution of authors
(in %) based on $h$ and $h_{c}$ for both Scopus and WoS. The proportion of
authors having $h\leq 10$ is higher in WoS for all disciplines. In
disciplines,Social Sciences has highest count ( 35.3%) and Biochemistry and
Molecular Biology has lowest count (11.4%) for authors with $h\leq 10$ for
both Scopus and WoS. Further, a significant change is noticed in Health and
Medical Sciences, and Natural Sciences where the authors ranked $h\leq 10$
shows 5% change in ranking from $h$ to $h_{c}$. For rest of the disciplines
the change is between 2-3%.

Further, the shift in the author’s ranking measured through the Spearman’s
rank correlation between $h$ and $h_{c}$ for both Scopus and WoS is given in
Table 5. Spearman’s rank correlation computes the association among two ranked
variables. The initial rank of the author is $h$-index and the updated rank of
the author is $h_{c}$ within a discipline for both Scopus and WoS. The major
fluctuations are in the category of $h\leq 10$. Both Biochemistry and
Molecular Biology, and Natural Sciences show large variation in Scopus and
WoS. Major fluctuations are measured in Biochemistry and Molecular Biology,
Health and Medical Sciences, and Social Sciences. Overall in Biochemistry and
Molecular Biology WoS performs better than Scopus and in Health and Medical
Sciences Scopus performs better than WoS. Hence, the performance of both
Scopus and WoS varies among disciplines.

Figure 5: Discipline-wise proportion of the number of authors with varying $h$ and $h_{c}$ in five disciplines for (a) Scopus and (b) WoS.  Table 4: Proportion of authors in five disciplines for varying $h$ and $h_{c}$ for Scopus (S) and WoS (W). Disciplines | ID | No. of Authors [%]
---|---|---
$h\leq 10$ | $11\geq h\leq 20$ | $21\geq h\leq 30$ | $31\geq h\leq 40$ | $41\geq h\leq 50$ | $h>50$
h | $h_{c}$ | h | $h_{c}$ | h | $h_{c}$ | h | $h_{c}$ | h | $h_{c}$ | h | $h_{c}$
Biochemistry and Molecular Biology | S | 11.4 | 10.2 | 33.0 | 31.8 | 29.5 | 31.8 | 12.5 | 12.5 | 8.0 | 8.0 | 5.7 | 5.7
W | 15.9 | 12.5 | 30.7 | 30.7 | 28.4 | 31.8 | 15.9 | 14.8 | 3.4 | 4.5 | 5.7 | 5.7
Engineering | S | 23.3 | 20.0 | 35.0 | 38.3 | 21.7 | 21.7 | 8.3 | 8.3 | 8.3 | 8.3 | 3.3 | 3.3
W | 30.0 | 28.3 | 33.3 | 35.0 | 18.3 | 18.3 | 10.0 | 10.0 | 5.0 | 5.0 | 3.3 | 3.3
Health and Medical Sciences | S | 25.5 | 19.8 | 34.0 | 38.7 | 18.9 | 19.8 | 10.4 | 9.4 | 4.7 | 5.7 | 6.6 | 6.6
W | 28.3 | 23.6 | 34.0 | 38.7 | 17.0 | 17.0 | 9.4 | 7.5 | 5.7 | 7.5 | 5.7 | 5.7
Natural Sciences | S | 19.6 | 15.2 | 37.0 | 39.1 | 23.9 | 26.1 | 10.9 | 10.9 | 8.7 | 8.7 | 0.0 | 0.0
W | 23.9 | 19.6 | 32.6 | 37.0 | 23.9 | 23.9 | 10.9 | 10.9 | 8.7 | 8.7 | 0.0 | 0.0
Social Sciences | S | 35.3 | 31.8 | 35.3 | 36.5 | 16.5 | 18.8 | 7.1 | 7.1 | 2.4 | 2.4 | 3.5 | 3.5
W | 43.5 | 40.0 | 30.6 | 32.9 | 16.5 | 17.6 | 5.9 | 5.9 | 0.0 | 0.0 | 3.5 | 3.5
Table 5: Spearman’s rank correlation shows the changes among the ranking. Disciplines | ID | Spearman’s rank correlation between $h$ and $h_{c}$
---|---|---
h$\leq$10 | 11$\geq$h$\leq$20 | 21$\geq$h$\leq$30 | 31$\geq$h$\leq$40 | 41$\geq$h$\leq$50 | h$>$50
Biochemistry and Molecular Biology | S | 0.77 | 0.96 | 0.96 | 0.97 | 0.96 | 1.00
W | 0.85 | 0.96 | 0.95 | 0.98 | 1.00 | 1.00
Engineering | S | 0.90 | 0.98 | 1.00 | 1.00 | 1.00 | 1.00
W | 0.93 | 0.98 | 1.00 | 1.00 | 1.00 | 1.00
Health and Medical Sciences | S | 0.92 | 0.93 | 0.94 | 0.97 | 1.00 | 1.00
W | 0.91 | 0.96 | 0.86 | 0.96 | 1.00 | 1.00
Natural Sciences | S | 0.83 | 0.95 | 1.00 | 1.00 | 1.00 | -
W | 0.87 | 0.92 | 1.00 | 1.00 | 1.00 | -
Social Sciences | S | 0.93 | 0.96 | 0.96 | 1.00 | 1.00 | 1.00
W | 0.92 | 0.94 | 0.95 | 1.00 | - | 1.00

Further, we have computed the difference between Scopus $h$-index and WoS
$h$\- index and calculated the standard deviation of the data for all five
disciplines. Similarly, the standard deviation is calculated for $h_{c}$ and
is shown in Figure 6. The deviation in Biochemistry and Molecular Biology and
in Natural Sciences is same. The deviation is slightly lower for Engineering
and Social Sciences whereas it is slightly higher for Health and Medical
Sciences. In general, $h_{c}$ is not much deviated from $h$ and the results
show a slight improvement to $h$ especially to lower-ranked profiles.

Figure 6: Discipline-wise standard deviation of $h$ and $h_{c}$. The deviation
is computed on the difference between Scopus $h$-index and WoS $h$\- index
(filled square) and Scopus $h_{c}$ and WoS $h_{c}$ (filled up-triangle).

##  4 Discussion and conclusion

In this study, we have extended the pioneering work of J. E. Hirsch by simply
focusing on one of the limitations of the $h$-index (Costas and Bordons, 2007;
Egghe, 2010). $h$-index focuses on both quantity and impact of publications
but ignored the impact of highly cited papers which under-estimates the
importance of the work. After the introduction of the $h$ index, many variants
of $h$ have been proposed by scientists in order to improve the research
evaluation of an individual (Schreiber, 2010). Some became meaningful like the
$g$-index; however, each and every index is lacking in one or the other sense.
Based on the $h$-index we have introduced $h_{c}$ which is a complementary
approach to the $h$-index. $h_{c}$ takes care of one of the limitations of the
$h$-index, especially $h$ ignores the highly cited papers. $h_{c}$ works on
$h$-index by adding weight to the highest cited paper of an individual. The
main goals of the study are: (i) to overcome the limitation of $h$-index by
taking into account the weight of the highest cited paper; (ii) an improvement
to $h$-index which significantly improve the ranking of scientists having
lower rank within a discipline; (iii) to analyze the impact of different
databases on the authors ranking based on $h$-index; and (iv) to analyze the
impact of the databases on different disciplines which in turn affect the
ranking of scientists.

Hirsch mentioned that the $h$-index cannot be compared among scientists of
different disciplines. In our study, we have worked on five disciplines to
check how the ranking of authors based on the $h$-index varies among Scopus
and WoS. The new index $h_{c}$ is computed on the same ranking and we found
that in total the major fluctuations appeared for the authors ranked $h\leq
10$ for both Scopus and WoS; however, this variation/fluctuation is higher in
WoS as compared to Scopus. In discipline-wise analysis, the results vary among
Scopus and WoS. For Engineering, Health and Medical Sciences, and Natural
Sciences, WoS shows less variation as compared to Scopus. On the other hand,
in Biochemistry and Molecular Biology, and Social Sciences Scopus has less
variation as compared to WoS. Hence, in discipline-wise analysis WoS gives
better ranking in some disciplines and in other Scopus does; however, the
overall performance of Scopus is measured better.

The advantage of $h_{c}$ is that it is not sensitive to disciplines. Also, in
some cases $h_{c}$ has performed better than $g$ too. Due to its simplicity
and in complement to $h$-index, $h_{c}$ could provide a useful insight towards
the young or lower-ranked authors which in turn significantly improves the
ranking of an individual within a discipline. It could be helpful in an
institution/ university for the internal ranking of the faculties within a
discipline. It also highlights the importance of the work carried out by an
individual as it takes into account the $h$-index along with the contribution
of the highest-cited paper. The present work has some limitations too. The
number of authors for the analysis of Engineering and Natural Sciences
disciplines is a bit low; however, we are able to get the essence of the
ranking. The larger sample can increase the universality of the results. For
future study, the same concept can be extended towards the ranking of the
organizations and journals.

## Acknowledgment

Both Scopus and WoS data has been downloaded from the Northwestern University,
USA.

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