Using the strength coecient(SC) to evaluate the most number of publications in research aliations involving COVID-19 till April 14, 2020: A bibliometric analysis

Background: When the COVID-19 outbreak spreads to the world, many articles related to it have been published in academics. Since the largest quantity of conrmed cases was reported in China till April 14, 2020, whether the number of Chinese articles of research associated with the COVID-19 topped globally is required to be examined. Thus, an objective measure determining the dominant role in a group should be dened. This study aims to propose an index (strength coecient, SC) to evaluate the most inuential research aliations in publications of COVID-19. Methods: We simulated data to verify the separation index that can be viable in use for determining the dominant one that has the absolute advantage in a group. We selected 4,369 articles as of April 14, 2020, with abstracts from the Pubmed Central (PMC) based on the keywords COVID-19 or 2019-nCOV. An author-weighted scheme (AWS) was applied to quantify coauthor credits in the article byline. Social network analysis incorporated with SC(from 0 to 1.0 and cutoff=0/70) was applied to display the inuential (1) article types, (2)countries, (3)medical subject headings(MeSH terms), and (4) research aliations. Visual dashboards were created for displaying the results on Google Maps. Results: We observed that the top one(SC) in each topic consists of (1) journal article(0.81), (2) China(0.61),(3) Acad Radol, (4) betacoronavirus (0.66), and (5) Hazhong University of Science and Technology(0.77) in article types, countries, journals, MeSH terms, and research aliations, respectively. Conclusion: We applied the SC to identify the strength of the top one over the next two. The SC was useful The are further in


Background
An index that can verify the dominant role in a group was required to obtain [1], such as the strength of the leading company in an industry. The Her ndahl index(known as HHI [2]) has been proposed to measure the strength of competition in industry [3]. However, The HHI de ned as the sum of the squares of the market shares of the rms(i.e., H= , where the number in the industry; n as that sometimes limited to the 50 largest rms) has some disadvantages. For instance, the market shares are constructed by many fractions. The HHI is uctuated without a common criterion (e.g., H= 0.33 = 3*(0.33*0.33) and H=0.25= 4*(0.25*25)for three and four equal-size companies, respectively).
Similarly, the Gini coe cient [4] was suggested to measure the author's research domain based on the top ve medical subject headings(MeSH terms) [5,6]. The major problem of these HHI and Gini is that all elements(or fractions) are equally considered(or weighted) in a formula instead of focusing on the top one with the dominant role (i.e., the 100% monopoly or say the strength of the competition). The scenario is rather similar to what we investigate one questionnaire forming a unidimensional construct using Eigenvalues to de nition [7,8]. The dimension coe cient(DC) is de ned by the top three eigenvalues(λi) with the formula(=[( λ1/λ2)/(λ2/λ3)]/[1+[( λ1/λ2)/(λ2/λ3)]]) and criterion(≥ 0.70), where λi stands for the number of Eigenvalues in descending order [9,10], The ratio of DC is renamed as separation index(SI) [1] [or strength coe cient(SC) in this study] for representing the dominant extent to which the role plays in a set of entities. Whether the SC can also be applied to other elds(e.g., dominant research a liations) is required for veri cation.
When the COVID − 19 spreads to the world, numerous articles related to COVID-19 have been published.
As of April 14, 2020, more than 4,369 documents were released in search of keyword "COVID-19 or 2019-nCov" in Pubmed Central(PMC). We are motivated to investigate the most in uential (1) article types, Ethical approval was not necessary for this study because all the data were extracted from the website publicly available in PMC.

Social network analysis
Social network analysis(SNA) [11] was applied to explore the pattern of entities in a system using the software Pajek [in Koeln; PajekMan in Osoje (Ossiach, Austria)] [12]. In keeping with the Pajek guidelines, we de ned an author research institute (or paper keyword) as a node (or an actor) that is connected to other nodes through the edge (or the relation). The number of connections usually de nes the weight between two nodes.
Centrality is a vital index for analyzing a network. Any individual or keyword in the center of a social network will determine its in uence on the network and its speed at gaining information [13,14]. In this study, we used the centrality degree as the number of weights connected to other nodes.

2/4 The Author-Weighted Scheme
The author-weighted scheme(AWS)[15] is applied to weight the author research institute: Where, considering a paper of m + 1 authors with the last being the corresponding author, Wj denotes the weight for an author on the order j in the article byline. The power, γj, is an integer number from m-1 to 0 in descending order. The sum of author weights in a byline is shown below: The sum of authorships for each paper equals 1.0. which is a basic concept ensuring that all papers have an equal weight irrespective of the number of coauthors [16]. As such, more importance is given to the rst (exp[m], primary) and the last (exp[m-1], corresponding or supervisory) authors, whereas it is assumed that the others (the middle authors) have made smaller contributions [17,18]. The smallest portion (exp(0) = 1) is assigned to the last second author with the odds = 1 as the basic reference [19,20].

Pattern of Authors' institute and countries o MeSH terms
We selected the topic of COVID-19 as the target article. A total of 4,369 articles (see Additional File 1) were collected. Five types of social networks were constructed, including (1) article types, (2)countries,(3) journals associated with counties, (4) MeSH terms, and (4) research a liations. The top three were highlighted in each network to compute the SC for each dominant role.

Creating Dashboards on Google Maps
Author-made online modules were used to present the dominant role of each network. We created pages of HTML used for Google Maps. All the relevant information on the entities (i.e., research institutes, MeSH

Results
The top ones(with SC) in each network are shown in gures from 1 to 5. It can be seen that (1)  All of those SCs, but the article type, were computed by the weights in their networks. The SC for article types are based on the on article counts weighted by the AWS (Table 1)  We applied the SC to represent the extent to which an entity plays a dominant role in a group. The SC concept is originated from test theory for identifying a one-dimension scale on an underlying construct [7][8][9][10].
The The latest public health information on COVID-19 has been released from Centers for Disease Control and Prevention (CDC) and National Institutes of health (NHI) [21][22][23][24]. Over 1,674 articles were found in PMC when the keyword "social network analysis" was searched as of April 14, 2020, and 444 with "social network analysis" in the title. We particularly applied SNA to extract information about the association among entities in publications on COVID-19, which is novel and rarely seen on the topic of COVID-19.
The second feature is about the AWS used for quantifying author contributions to the article. In this study, AWS was applied to authors' origin countries and research a liations. Others link MeSH terms and article types are assumed each entity with equal credit in an article.

Availability of data and materials
All data used in this study are available in Additional les.

Competing interests
Page 8/15 The authors declare that they have no competing interests.

Funding
There are no sources of funding to be declared.

Authors' Contributions
WC developed the study concept and design. JCJL and YT analyzed and interpreted the data. TWC monitored the process of this study and helped in responding to the reviewers' advice and comments. TWC drafted the manuscript, and all authors provided critical revisions for important intellectual content. The study was supervised by TWC. All authors read and approved the nal manuscript.