**3. Influential Contributor Analyses**

According to Table 4, the frequency of the most cited paper is 183; it reviewed old and new methods of measuring fluctuation asymmetry and then reviewed the theory, developmental origins, and the applications of fluctuation asymmetry [26].

The paper "Inflationary cosmology in modified gravity theories" was cited 175 times; it reviewed inflationary cosmology in modified gravity [27]. The paper "Analyzing fluctuating asymmetry with geometric morphometrics: concepts, methods, and applications" ranks third place and was cited 125 times. The theme of this paper is the same as the most cited paper, i.e., fluctuating asymmetry. This paper summarized the concepts and morphometric methods for studying fluctuating asymmetry of shape and size.

In the top 15 most cited papers, we can find that there are only 2 papers published in recent years (in 2018); thus, the papers published in recent years still need time to gain attention. These data illustrate that the top 15 most cited papers all promote the development and advance of the journal and the related research fields. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 8 of 19 Figure 4 depicts the cooperation network among countries/regions, where the nodes represent

Figure 4 depicts the cooperation network among countries/regions, where the nodes represent the countries/regions, and the sizes denote the citations; that is, the larger the size of the node, the greater the number of citations. The lines between two countries/regions denote that they cooperate. The density of the links of a country indicates the cooperation degree. The denser of the lines, the more collaboration for one country with other countries. From Figure 4, we can see that China, the USA, Pakistan, and the UK have more lines. Therefore, they have more cooperation with other countries. the countries/regions, and the sizes denote the citations; that is, the larger the size of the node, the greater the number of citations. The lines between two countries/regions denote that they cooperate. The density of the links of a country indicates the cooperation degree. The denser of the lines, the more collaboration for one country with other countries. From Figure 4, we can see that China, the USA, Pakistan, and the UK have more lines. Therefore, they have more cooperation with other countries.

**Figure 4.** The co-authorship network of countries/regions. **Figure 4.** The co-authorship network of countries/regions.

Table 5 gives the top 10 most influential countries/regions and their corresponding data. China has the most citations (4002) and the highest H-index (24), which is consistent with Figure 4. For ≥100, each of the USA, Spain, the UK, Japan, and Italy has one paper. Furthermore, it can be seen that 5 Table 5 gives the top 10 most influential countries/regions and their corresponding data. China has the most citations (4002) and the highest H-index (24), which is consistent with Figure 4. For ≥100, each of the USA, Spain, the UK, Japan, and Italy has one paper. Furthermore, it can be seen that 5

papers from China have more than 50 citations, 36 papers have more than 20 citations, and 86 papers

journal. It is noted that, although the UK only has 96 publications on *Symmetry*, it has the highest AC with 7.28, which means that these papers play an important role in the related research fields. China and Saudi Arabia have 10 high-cited papers each. We also find that the top 10 most influential

**Table 5.** The top 10 most influential countries/regions.

1 China Asia **1226 4002** 3.26 **24** 0 5 36 86 10 0

3 Pakistan Asia 207 1179 5.70 17 0 2 15 74 7 2 4 South Korea Asia 340 1011 2.97 15 0 0 9 61 1 0 5 Spain Europe 217 851 3.92 11 1 3 5 18 1 0 6 Saudi Arabia Asia 177 781 4.41 13 0 2 11 25 10 2 7 UK Europe 96 699 **7.28** 12 1 4 7 15 1 0 8 Japan Asia 107 669 6.25 12 1 3 5 17 1 0

341 1718 5.04 19 1 3 16 91 3 0

**H C 1**

**HP** 

**Countries Continent TP TC AC H-Index** ≥**100** ≥**50** ≥**20** ≥**10** 

countries/regions are mainly from Asia and Europe.

North American

2 USA

papers from China have more than 50 citations, 36 papers have more than 20 citations, and 86 papers have more than 10 citations. There are 91 papers from the USA with more than 10 citations, which are far more than other countries. Thus, China and the USA are two biggest contributors to this journal. It is noted that, although the UK only has 96 publications on *Symmetry*, it has the highest AC with 7.28, which means that these papers play an important role in the related research fields. China and Saudi Arabia have 10 high-cited papers each. We also find that the top 10 most influential countries/regions are mainly from Asia and Europe.


**Table 5.** The top 10 most influential countries/regions.

<sup>1</sup> HC: the number of the high-cited papers; HP: the number of the hot papers, the same below.

Furthermore, the top 10 most cited institutions are presented in Table 6. The University of New Mexico is the most cited institution, with 491 citations and 11 H-index, while its AC is only 9.63. Sichuan Normal University has 362 citations and ranks in second place. The University of Manchester has the greatest AC (43.30), even though it only has 5 papers, which explains the importance of these papers and the related research topics. Its most cited paper, *Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications*, is the third most cited paper of *Symmetry*.


**Table 6.** The top 10 most influential institutions.

Next, the most cited authors are analyzed and the top 10 most influential authors are presented in Table 7. Smarandache F. has the greatest TC and H-index, ranking in the first place. Besides, even though each of Hel-Or Hagit, Nevo Eviatar, and Raz Shmuel only published two papers in *Symmetry*, their AC is the highest (95.50). Furthermore, they relate to the same paper, i.e., *Fluctuating Asymmetry: Methods, Theory, and Applications*, the most cited paper in Table 4. Graham, John H. ranks in second place of AC and is also the author of the same paper. This phenomenon can be explained by the cooperative relationship among authors. Then, we analyze the cooperation relationship and depict the corresponding science mapping as shown in Figure 5.


(1244). Then, Zhang X. H. has 16 links and a total link strength of 56, 4.5% of 1244.

**Table 7.** The top 10 most influential authors.

**Figure 5.** The closest cooperation relationship among authors in *Symmetry.* **Figure 5.** The closest cooperation relationship among authors in *Symmetry*.

**4. The Co-Citation and the Burst Detection Analysis**  In this section, we make co-citation and the burst detection analysis by depicting visualizations combining with VOSviewer and CiteSpace. The co-citation analyses are conducted from the following aspects: reference co-citation, source co-citation, and author co-citation. Citation burst detection reflects the explosive data, that is, in a certain period, scholars' attention is attracted [29]. Figure 6 illustrates the closest reference co-citation network, where the threshold that denotes The visualization of the cooperation network only presents 296 authors, which is the closest network by setting the minimum number of documents of an author as two. In Figure 5, the size of the node denotes the number of citations, for example, the node for Smarandache F., is the largest, followed by Wei G. W., which is consistent with Table 7. Besides, the links between the two authors mean that they cooperate. The links linked to Smarandache F. are the greatest, therefore having 43 links, 6.1% of the total links (704), and their total link strength is 99, 8% of the whole link strength (1244). Then, Zhang X. H. has 16 links and a total link strength of 56, 4.5% of 1244.

#### the minimum number of citations of a cited reference is 20, and there are 31 references that satisfy the threshold. The closest network includes 25 references. In Figure 6, a node shows a reference, the size **4. The Co-Citation and the Burst Detection Analysis**

of the node denotes the citations number of the references. A link between two references means a co-citation relationship. The thicker the link is, the more citations the reference has. There are 5 clusters marked with different colors. Furthermore, the paper *Fuzzy sets, Information Control, 1965, 8, 2–3: 30–33* (cited 38,108 times) ranks in first place, with 203 citations in *Symmetry*. Similarly, the author In this section, we make co-citation and the burst detection analysis by depicting visualizations combining with VOSviewer and CiteSpace. The co-citation analyses are conducted from the following aspects: reference co-citation, source co-citation, and author co-citation. Citation burst detection reflects the explosive data, that is, in a certain period, scholars' attention is attracted [29].

and source co-citation networks are also be displayed. Then, Table 8 presents the top 10 most cited references/sources/authors by publications in *Symmetry*. Figure 6 illustrates the closest reference co-citation network, where the threshold that denotes the minimum number of citations of a cited reference is 20, and there are 31 references that satisfy the threshold. The closest network includes 25 references. In Figure 6, a node shows a reference, the size of the node denotes the citations number of the references. A link between two references means a co-citation relationship. The thicker the link is, the more citations the reference has. There are 5

clusters marked with different colors. Furthermore, the paper *Fuzzy sets, Information Control, 1965, 8, 2–3: 30–33* (cited 38,108 times) ranks in first place, with 203 citations in *Symmetry*. Similarly, the author and source co-citation networks are also be displayed. Then, Table 8 presents the top 10 most cited references/sources/authors by publications in *Symmetry*. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 11 of 19

**Figure 6.** The closest co-citation network of references in *Symmetry.* **Figure 6.** The closest co-citation network of references in *Symmetry*.


**Table 8.** The top 10 most cited references/sources/authors by publications in the journal.

*Neutroso Sc.* 867 Wei, G.W. 267 6 Wang H., 2010, *Multispace Multistru* 43 *Phys. Lett. B* 862 Xu, Z.S. 241 7 Ye J, 2014, *J. Intell. Fuzzy Syst.* 42 *Fuzzy Set. Syst.* 816 Kim, T 229 8 Atanassov K, 1989, *Fuzzy Set. Syst.* 38 *Expert Syst. Appl.* 778 Zhang, X.H. 229 Table 8 lists the information of the top 10 most cited references/sources/authors by publications in *Symmetry*. Six of references are published before 2010, and the first cited reference is from 1965 by Zadeh [30]. Only two references had a number of citations more than 100. *Phys. Rev. D* ranks the first cited source with 2226 citations. In terms of cited authors, Ye, J. H. received the most citations, with 336, followed by Smarandache, F (331) and Zadeh, La (307).

9 Pawlak Z, 1982, *Int. J. Comput. Inf. Sci.* 35 *J. Intell. Fuzzy Syst.* 735 Atanassov, K.T. 184 10 Wang H., 2005, *Interval Neutrosophi* 31 *Phys. Rev. A* 728 Kostelecky, V.A. 176 Through detecting bursts, Table 9 lists the top 10 cited authors of publications in *Symmetry* with the strongest citation bursts. Zadeh La on the top of the list with the maximum burst strength of 17.965. All of them have a citation burst duration with three years and close to the present (from 2018 to 2019), which shows that their work may have formed a hot and leading topic.

Table 8 lists the information of the top 10 most cited references/sources/authors by publications in *Symmetry*. Six of references are published before 2010, and the first cited reference is from 1965 by Zadeh [30]. Only two references had a number of citations more than 100. *Phys. Rev. D* ranks the first cited source with 2226 citations. In terms of cited authors, Ye, J. H. received the most citations, with

Through detecting bursts, Table 9 lists the top 10 cited authors of publications in *Symmetry* with the strongest citation bursts. Zadeh La on the top of the list with the maximum burst strength of 17.965. All of them have a citation burst duration with three years and close to the present (from 2018

**Cited Authors Year Strength Begin End 2009–2019**  1 Zadeh La 2009 17.965 2018 2019 ▂▂▂▂▂▂▂▂▂▃▃

to 2019), which shows that their work may have formed a hot and leading topic.

336, followed by Smarandache, F (331) and Zadeh, La (307).


**Table 9.** Top 10 cited authors with the strongest citation bursts.

Table 10 presents the top 15 cited journals with the strongest citation bursts from 2009 to 2019. The cited journals receive frequent citations by *Symmetry* in a certain period. The citation bursts of the cited journals of Inform. Control. had the longest strength (39.1302). Besides, 5 of the top 15 cited journals had the longest duration, with 8 years from 2009 to 2016, which means that the publications in *Symmetry* cited these journals earlier and explosively. Of these 15, 7 are the closest to 2019, such as *Inform. Control*., *Knowl-Based Syst*., and *IEEE T. Fuzzy Syst*., which illustrates that they still have an influence on *Symmetry* and can even influence the future research directions.


**Table 10.** Top 15 cited journals with the strongest citation bursts.
