**1. Introduction**

The bibliometric method has been widely applied in exploring publications' structure and the development of a journal. In recent years, scholars have systematically researched journals, such as *European Journal of Operational Research* [1], *Technological and Economic Development of Economy* [2], *Information Sciences* [3], *IEEE Transactions on Fuzzy Systems* [4], *International Journal of Strategic Property Management* [5], *Journal of Civil Engineering and Management* [6], and *Baltic Journal of Road and Bridge Engineering* [7]. The development trends of various research topics are also conducted, related to fuzzy decision making [8], sustainable energy [9], support vector machines [10], etc. Combining with visualization tools, i.e., VOSviewer [11,12], CiteSpace [13–15], CiteNetExplorer [16], Bicomb [17,18], BibExcel [19,20], etc., the science mapping enriches the contents of bibliometric analyses from co-citation, co-occurrence, co-authorship, and burst detection aspects. It also helps scholars intuitively grasp research trends greatly and main research focuses in different phases [21]. In this paper, VOSviewer and CiteSpace are used to demonstrate the characteristics of the journal. The former conducts the co-citation analysis, co-authorship analysis, and co-occurrence analysis, aiming to present the structure

of publications. The latter is chosen to cluster keywords and track development trends in different years of the journal by cluster analysis, burst detection analysis, and timeline analysis.

*Symmetry* is an international open-access journal indexed by the Science Citation Index Expanded (Web of Science, search for "*Symmetry-Basel*"), Scopus, MathSciNet (American Mathematical Society), and other databases with an impact factor of 2.645 by Journal Citation Reports (2019). It covers research on symmetry phenomena in scientific studies, including physics, chemistry, biology, mathematics, computer science, theory and method, etc. The details are listed as Table 1:


**Table 1.** The subject areas of *Symmetry*.

To date, *Symmetry* has published over 3000 documents with the development of 12 years. Therefore, it is valuable to explore the development trend based on bibliometric methods and science mapping. Since the first paper published in *Symmetry* in 2009, we analyze the journal from 2009 to 2019 mainly from following aspects (considering the completeness of data, we only searched the publications from 2009 to 2019): (1) the basic characteristics of publications are presented to describe development status, including the type of publications, annual number, citation number, and the productive contributors; (2) the top 15 most cited papers are listed. The influential countries/regions, institutions, and authors in the journal are provided, based on the total number of publications (TP), the total number of citations (TC), the number of citation-year distribution (C), the number of average citation (AC), H-index, the number of publications that satisfy certain citations (i.e., ≥100, ≥50) [22,23], etc. Besides, we also analyze the important cooperation relationship; (3) the co-citation analyses at the level of reference/source/authors, the burst detections of cited authors and cited journals, and the co-occurrence analyses and timeline view analysis of keywords are given, which is conducive to clear the development directions and the changes of research focus; (4) the future challenges of *Symmetry* are also discussed, combining with the above results.

The rest of this paper is organized as follows: Section 2 illustrates the data source and analyzes the basic characteristics, i.e., publications, citation numbers, and citation structure. The influential contributors in terms of papers, countries/regions, institutions, and authors are presented in Section 3. The co-citation and burst detections analyses are given in Section 4. Section 5 focuses on the co-occurrence and timeline view analyses of keywords. Section 6 discusses the characteristics of this journal and presents future suggestions according to the whole analyses. Some conclusions are provided to end this paper in Section 7. The rest of this paper is organized as follows: Section 2 illustrates the data source and analyzes the basic characteristics, i.e., publications, citation numbers, and citation structure. The influential contributors in terms of papers, countries/regions, institutions, and authors are presented in Section 3. The co-citation and burst detections analyses are given in Section 4. Section 5 focuses on the cooccurrence and timeline view analyses of keywords. Section 6 discusses the characteristics of this

journal and presents future suggestions according to the whole analyses. Some conclusions are

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 3 of 19

#### **2. Data Source and Basic Characteristics** provided to end this paper in Section 7.

This paper mainly uses the bibliometric method to study the publications in *Symmetry* from 2009 to 2019. The literature data are from the Web of Science (WoS) Core Collection database on June 24, 2020, using *Symmetry-Basel* (we replace *Symmetry-Basel* with *Symmetry* below). Then, through the search for the journal's name, we found 3125 papers. **2. Data Source and Basic Characteristics**  This paper mainly uses the bibliometric method to study the publications in *Symmetry* from 2009 to 2019. The literature data are from the Web of Science (WoS) Core Collection database on June 24, 2020, using *Symmetry-Basel* (we replace *Symmetry-Basel* with *Symmetry* below). Then, through the

Base on the analytic results given by WoS, we obtain Figure 1 and find that the paper types published on *Symmetry* are classified into five kinds. The number of articles is 2941 and far more than other types of publications. This is followed by 161 reviews, 21 editorial material, 2 corrections, and 1 biographic item. This phenomenon shows that *Symmetry* focuses on academic articles. Then, the total number of publications (TP), the total number of citations distribution (TC), and the number of citation-year distribution (C) in the journal from 2009 to 2019 are illustrated in Figure 2. In this paper, we also use AC to denote the average number of citations per publication. search for the journal's name, we found 3125 papers. Base on the analytic results given by WoS, we obtain Figure 1 and find that the paper types published on *Symmetry* are classified into five kinds. The number of articles is 2941 and far more than other types of publications. This is followed by 161 reviews, 21 editorial material, 2 corrections, and 1 biographic item. This phenomenon shows that *Symmetry* focuses on academic articles. Then, the total number of publications (TP), the total number of citations distribution (TC), and the number of citation-year distribution (C) in the journal from 2009 to 2019 are illustrated in Figure 2. In this paper, we also use AC to denote the average number of citations per publication.

**Figure 1.** Types of the *Symmetry* publications. **Figure 1.** Types of the *Symmetry* publications.

From Figure 2a, the annual number of publications per year shows an increasing trend. To be specific, the annual publications were less than 100 before 2015. Then, it has been increasing rapidly, and the annual publications have been greater than 1000 in 2019, which shows that more and more scholars have paid attention to the journal. From Figure 2a, the annual number of publications per year shows an increasing trend. To be specific, the annual publications were less than 100 before 2015. Then, it has been increasing rapidly, and the annual publications have been greater than 1000 in 2019, which shows that more and more scholars have paid attention to the journal.

Furthermore, Figure 2a describes the citation numbers of papers published in each year. The publications receive the most citations (3324) in 2018, followed by 2234 citations in 2019, and 1930 citations in 2017. The trend of citations had three peaks, i.e., in 2010 (1388), 2015 (918), and 2018 (3324), respectively. Figure 2b illustrates the citation numbers of each year from 2009 to 2019. We can see that the citation-year distributions increased year by year. In 2009, the number of citations was only 3; since 2011, the annual number of citations was more than 100. By 2018, the number of citations increased to 1840, which denotes that *Symmetry* was paid close attention. The low citation-year, i.e., 2013, does not mean that no excellent studies appeared; the number of citations is dynamic and time is required for publications to be widely recognized and cited [24]. Table 2 is provided to explore more detailed information about *Symmetry*. Among the several indicators, H-index considers both the number of publications and citations; the index without self-citations is an important indicator. A high H-index

implies a greater achievement [25]. Furthermore, different intervals reflect the number of citations; for example, ≥50 denotes the number of publications that cited times great than or equal to 50. From Table 2, the paper published in 2018 has the greatest TC (3324) and H-index (24), 2010 has the greatest AC (18). It is obvious that as time goes by, the influence of *Symmetry* has increased. Based on the data collection from WoS, only in 2010 and 2015 were there two papers that satisfy the standard of "≥100", and three papers were high-cited papers. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 4 of 19

**Figure 2.** The number of publications and citations distribution. **Figure 2.** The number of publications and citations distribution.


publications receive the most citations (3324) in 2018, followed by 2234 citations in 2019, and 1930 **Table 2.** *Symmetry* publication characteristics from 2009 to 2019.

Furthermore, Figure 2a describes the citation numbers of papers published in each year. The

increased. Based on the data collection from WoS, only in 2010 and 2015 were there two papers that satisfy the standard of "≥100 ", and three papers were high-cited papers. <sup>1</sup> TP: total number of publications; TC: the total number of citations distribution; AC: the average number of citations per publication, the same below.

2009 15 106 7 6 0 0 2 4 6

**Year TP** <sup>1</sup>

Next, this paper analyzes the productive objects, including countries/regions, institutions, and authors. The countries/regions with greater than 100 publications are presented in Figure 3 and then the top 10 productive institutions and authors are presented in Table 3. From Figure 3, we can see that the scholars in China have published 1226 papers and rank in the first place. Following, the scholars in the USA and South Korea both published more than 340 papers each, and rank in the second and the third places, respectively. The fourth to eleventh productive countries/regions are Spain (217), Pakistan (207), Saudi Arabia (177), Italy (118), Malaysia (114), Poland (109), Japan (107), and India (106). Next, this paper analyzes the productive objects, including countries/regions, institutions, and authors. The countries/regions with greater than 100 publications are presented in Figure 3 and then the top 10 productive institutions and authors are presented in Table 3. From Figure 3, we can see that the scholars in China have published 1226 papers and rank in the first place. Following, the scholars in the USA and South Korea both published more than 340 papers each, and rank in the second and the third places, respectively. The fourth to eleventh productive countries/regions are Spain (217), Pakistan (207), Saudi Arabia (177), Italy (118), Malaysia (114), Poland (109), Japan (107), and India (106).

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2010 78 1388 **18** 18 2 8 16 35 48 2011 40 392 10 12 0 1 4 14 20 2012 33 201 6 7 0 1 0 4 9 2013 13 38 3 4 0 0 0 0 2 2014 50 457 9 9 0 3 5 9 24 2015 114 918 8 13 2 0 8 20 41 2016 158 736 5 14 0 0 7 20 50 2017 323 1930 6 20 0 1 21 57 128 2018 772 **3324** 4 **24** 0 3 31 74 210 2019 **1529** 2234 1 15 0 3 10 37 109 Total 3125 11724 - - 4 20 104 274 647

In terms of institutions, China Medical University Taiwan published 66 papers and ranks first, followed by the National University of Defense Technology China (59), Beijing Jiaotong University (54), King Abdulaziz University (52), and the University of New Mexico (51), respectively. In the top 10 institutions, 6 of them are from China. In terms of institutions, China Medical University Taiwan published 66 papers and ranks first, followed by the National University of Defense Technology China (59), Beijing Jiaotong University (54), King Abdulaziz University (52), and the University of New Mexico (51), respectively. In the top 10 institutions, 6 of them are from China.

**Figure 3.** The 11 countries/regions with greater than 100 publications. **Figure 3.** The 11 countries/regions with greater than 100 publications.

On the author's side, Smarandache F., from the USA, and Zhang X. H., from China, rank first and second, with 51 and 31 publications, respectively. Among the top 10 most productive authors, 4 of them are from China, 4 come from South Korea, 1 comes from the USA, and the other is Vietnamese. From the above three aspects, *Symmetry* has aroused special attention for scholars from China, the USA, and Korea. On the author's side, Smarandache F., from the USA, and Zhang X. H., from China, rank first and second, with 51 and 31 publications, respectively. Among the top 10 most productive authors, 4 ofthem are from China, 4 come from South Korea, 1 comes from the USA, and the other is Vietnamese. From the above three aspects, *Symmetry* has aroused special attention for scholars from China, the USA,and Korea.



Furthermore, the subject areas of *Symmetry* relate to physics, chemistry, biology, computer science, theory and methods, etc., which is multidisciplinary. Since it published papers, some publications impact the corresponding field. Table 4 lists the details of the top 15 most influential papers, including author, type, year, citation, etc.



From Table 4, 5 publications are articles and 10 publications are reviews. The top three cited publications are all reviews [26–28] and high-cited papers. Furthermore, two of them are studying fluctuating asymmetry, which has been widely investigated from basic theories, methods, and applications. Besides, the top 15 most cited papers were mainly published in 2010 (7), 2014 (2), 2015 (2), and 2018 (2). Furthermore, 10 of them have more than one author. Thus, the cooperation of authors also plays a key role in academic research.
