A comparison of citation disciplinary structure in science between the G7 countries and the BRICS countries

The data source of the study is Bibmet (2017 Quarter 1 version), the bibliometric version of the Web of Science (WoS) at KTH Royal Institute of Technology (Sweden). Bibmet is a relational database, based on WoS raw data purchased from Clarivate Analytics. Bibmet, which is updated quarterly, contains about 51 million WoS publications from the publication year 1980 onwards. The database also includes citation relations between WoS source publications.

To compare the disciplinary structure over time, two publication years were used: 1993 and 2013. The year 2013 was selected in order to have a fairly recent end year, and at the same time ensuring that all (or almost all) citations from WoS publications to publications published in the end year were present in the Bibmet version used in the study. Further, we first used 2003 as start year, but since very small differences in disciplinary structure, compared to year 2013, were observed, we decided to use 1993 as start year instead. For citations, we used 3-year windows. For example, for the publication year 1993, the citation window is 1993–1995. The data were collected in the following way:

We used a list of journals obtained from the 2013 Journal Citation Reports Science Edition. This list was named JCR_list. JCR_list contains 8,534 journals, together with their ISSNs.

With reference to point 8 above, a publication might involve more than one country because of co-authorship. Due to this, we applied fractional counting of publications and citations. Since there are no associations in WoS between author names and addresses before the publication year 2008, address fractionalization was used. For instance, if a publication has two China addresses and three United States addresses, and if it has received 10 citations, China is assigned 2/5 and United States 3/5 of the publication, while China is assigned 2/5 × 10 = 4 and United States 3/5 × 10 = 6 citations.

In Table 2, journal and publication volume statistics are reported.

Table 2

Journal and publication volume by publication year.

As we use fractionalization, when we refer to the number of publications and the number of citations for countries, we actually mean magnitude of publication fractions and magnitude of fractions of citations counts, respectively.

For country i, we define P_ijy as the number of publications of i in field j in publication year y and C_ijy as the number of citations to i in j during the three-year window starting with y. Let P_jy (C_jy) be the total number of publications (citations) in j in y (during the three-year window staring with y). We then define R_Pijy and R_Cijy as

RPijy=PijyPjy×<!-- ? -->100$$\begin{array}{} \displaystyle R_{Pijy}=\frac{P_{ijy}}{P_{jy}}\times100 \end{array}$$(1)

RCijy=CijyCjy×<!-- ? -->100$$\begin{array}{} \displaystyle R_{Cijy}=\frac{C_{ijy}}{C_{jy}}\times100 \end{array}$$(2)

Thus, R_Pijy gives the percentage of the publications of country i in field j in publication year y relative to the total number of publications in j in y, whereas R_Cijy gives the percentage of the citations to country i in field j during the three-year window starting with y, relative to the total number of citations in field j during the three-year window starting with y.

The disciplinary structure of the publication volume for a country i in publication year y can now be operationalized as the vector V_Piy, whereas the disciplinary structure of the citations for country i for the three-year window starting with year y can be operationalized as the vector V_Ciy:

VPiy=RPi1y,RPi2y,…<!-- ? -->,RPiny$$\begin{array}{} \displaystyle V_{Piy}=\left(R_{Pi1y},R_{Pi2y},\ldots,R_{Piny}\right) \end{array}$$(3)

VCiy=RCi1y,RCi2y,…<!-- ? -->,RCiny$$\begin{array}{} \displaystyle V_{Ciy}=\left(R_{Ci1y},R_{Ci2y},\ldots,R_{Ciny}\right) \end{array}$$(4)

where n = 10.

The cosine measure (Salton & McGill, 1983) was applied to measure the similarity between the citation disciplinary structures for one country in different publication years (1993, 2013), and between such structures for different countries in the same publication year (2013):

Sim(VCiyVCi′y′)=∑<!-- ? -->j=110RCijy×<!-- ? -->RCi′jy′∑<!-- ? -->j=110RCijy2×<!-- ? -->∑<!-- ? -->j=110RCi′jy′2$$\begin{array}{} \displaystyle Sim(V_{Ciy}V_{Ci'y'})=\frac{\sum^{10}_{j=1}R_{Cijy}\times R_{Ci'jy'}}{\sqrt{\sum^{10}_{j=1}\left(R_{Cijy}\right)^2}\times\sqrt{\sum^{10}_{j=1}\left(R_{Ci'jy'}\right)^2}} \end{array}$$(5)

where i′ and c′ stand for a country and a year, respectively.

A cluster analysis was used to group countries based on cosine similarity values for pairs of countries. We used the average linkage, a well-known hierarchical method, for the clustering (Everitt et al., 2001). The Silhouette measure (Kaufman & Rousseeuw, 1990) was used in order to obtain the best number of clusters. This measure contrasts coherence to separation by comparing within-cluster dissimilarity to between-cluster dissimilarity. Since the measure is defined in terms of dissimilarities, we converted the cosine similarity values to corresponding dissimilarity values by subtracting a given similarity value from 1. The cluster solution with the highest overall Silhouette value turned out to have two clusters for publication volume disciplinary structure and five clusters for citation disciplinary structure.

It might be the case that there are G7 and/or BRICS countries that are more similar, with respect to the citation disciplinary structure, to countries outside the G7-BRICS group than to countries within this group. In order to have a more comprehensive view of the citation disciplinary structure patterns, we extended the set of countries used in the cluster analysis with the nine countries (apart from the G7-BRICS countries) with the largest publication volumes in 2013. Thus, 21 countries were used in the cluster analysis.

With regard to the comparison of the disciplinary structure of the publication volume and of the citations within a given country i, we are interested in the distance between the publication and citation percentages R_Pijy and R_Cijy (j = 1, …, 10). More precisely, we are interested in the distance between the vectors V_Piy and V_Ciy. The Jeffreys-Matusita distance (Bruzzone L.et al., 1995) was applied to measure the distance for a given country i in year 2013. This measure (with respect to publication year 2013 and for country i) is defined as:

Dist(VPi2013,VCi2013)=∑<!-- ? -->j=110RPij2013−<!-- - -->RCij201321/2$$\begin{array}{} Dist(V_{Pi2013},V_{Ci2013})=\left[\sum^{10}_{j=1}\left(\sqrt{R_{Pij2013}}-\sqrt{R_{Cij2013}}\right)^2\right]^{1/2} \end{array}$$(6)

Clearly, the Jeffreys-Matusita distance is similar to the well-known Euclidian distance. However, the latter is more dependent on the magnitudes of the components of the involved vectors. For instance, the Euclidian distance between two vectors with very small components, and thus with small norms, might underrate the distance between the vectors. In view of this, and in our context, we consider the Jeffreys-Matusita distance to be a better choice than Euclidian distance.

Moreover, in order to have a summary value for country i in publication year 2013 across all 10 fields, we calculated means of the elements of the vectors V_Pi2103 and V_Ci2013:

Mean(VPi2013)=110∑<!-- ? -->j=110RPij2013$$\begin{array}{} Mean(V_{Pi2013})=\frac{1}{10}\sum^{10}_{j=1}R_{Pij2013} \end{array}$$(7)

Mean(VCi2013)=110∑<!-- ? -->j=110RCij2013$$\begin{array}{} Mean(V_{Ci2013})=\frac{1}{10}\sum^{10}_{j=1}R_{Cij2013} \end{array}$$(8)

Figure 1 visualizes the outcome of the cluster analysis, which is based on the citation disciplinary structures of the G7 and BRICS countries, as well as on the corresponding structures of the nine countries, apart from the G7/BRICS countries, with the largest publication volumes in 2013. The clusters and countries are represented horizontally, whereas the 10 fields are represented vertically, with the field names located in the bottom of the figure (see Table 1 for the full names of the fields). The dendrogram for the analysis occurs to the right of the last column of the figure. Table 3 gives the R_Cij2013 values (Equation 2) across the 10 fields for the 21 considered countries for year 2013.

Figure 1

Table 3

R_Cij2013 values for 21 countries (2013).

For each country i and field j represented in Figure 1, the darkness of the corresponding grid is related to the value of R_Cij2013: the darker the color is, the larger the value is. Countries belonging to the same cluster tend to be represented by similar rows with respect to darkness levels across the fields. Thus, such countries tend to have similar citation disciplinary structures, given our operationalization of such structures.

For the 5-cluster solution, i.e. the solution with the highest overall Silhouette value, the G7 countries belong to the same cluster, together with Australia, Netherlands, South Africa and Switzerland, whereas the five BRICS countries are distributed over four groups. We observe that South Africa is the only BRICS country that belongs to the same cluster as the G7 countries. Thus, all the cluster neighbors of the other four BRICS countries are non-G7 countries. These results indicate that the G7 countries and BRICS countries are quite heterogeneous regarding citation disciplinary structure.

United States and United Kingdom are the two countries that are grouped first in the hierarchical clustering process Figure 1), which indicates that they are similar in citation disciplinary structure. Because the countries are grouped based on cosine similarity values, and cosine-based measure is independent of size effects and only focuses on the disciplinary profiles of the citations. The data in Table 3 suggest, in more detail, why they are similar: Both countries have their highest R_Cij2013 values in Space Science and Medicine, and their smallest value in Agriculture. As is visible in Figure 1, Germany, France and Italy are also grouped early in the process. Space Science is the strongest field for those three countries in terms of citation impact. For example, for Germany, the R_Cij2013 value of Space Science is 8.6%, while the R_Cij2013 value of other fields are lower than 8% (Table 3). Apart from Space Science, Italy and France are comparatively strong in Mathematics from a citation point of view. Table 3 shows that for France and for a majority of the fields, the R_Cij2013 value is lower than 4%, while the R_Cij2013 value for Mathematics exceeds 6%. Like Germany, France and Italy, Canada Australia and Switzerland are grouped early. For these three countries, Life Sciences (Medicine, Biology) and Earth Sciences (Environment/ Ecology, Geosciences) are prominent fields regarding citation impact.

For China and India, both grouped together early in the clustering process, the citation disciplinary structure is dominated by Chemistry and Engineering. For China, Chemistry and Engineering have R_Cij2013 values of about 25% and 24%, respectively, whereas the percentages in the other fields are less than 18%. Agriculture Sciences dominates for both Brazil and South Africa, even if the two countries do not belong to the same cluster until the next last step in the process has been executed, when the number of clusters is equal to 2 (Figure 2). For Brazil, the world share of Agriculture Science is 4.41%, compared to less than 2% in the other fields.

Figure 2

Also South Africa has a better performance in Agriculture Sciences compared to the other fields.

Note that Russia is not grouped with another country until the last step of the clustering process has been executed, when the number of clusters is equal to 1. This indicates Russia has unique citation disciplinary structure characteristics, relative to the other considered countries. Russia’s academic achievements in Mathematics and Physics are globally acknowledged. This is reflected by the citation disciplinary structure of Russia, where the R_Cij2013 values of these two fields are much higher compared to the other fields.

Table 4 gives similarity values, which are based on the citation disciplinary structures in 1993 and 2013, for the G7 countries and BRICS countries. A given value indicates the similarity between the 1993 and the 2013 citation disciplinary structures of the corresponding country. The closer the similarity value is to 1, the more similar are the citation disciplinary structures for a country with respect to the years 1993 and 2013.

Table 4

Similarity values based on citation disciplinary structures in 1993 and 2013.

It is clear from Table 4 that all cosine values, except the one for Brazil, are greater than 0.9. Thus, in general the citation disciplinary structures within countries changed to a small extent across the two considered years (the similarity value is equal to or greater than 0.95 for nine of the 12 countries). We can see that the similarity values of most G7 countries are slightly higher compared to a majority of BRICS countries. For most G7 countries, then, the citation disciplinary structure tend to be more stable compared to BRICS countries with regard to the periods 1993 and 2013.

China has a lower similarity value than the other countries, apart from Brazil (0.907, Table 4). Compared to the other G7 and BRICS countries, the citation disciplinary structures of Brazil and China are more dissimilar regarding the two years. In view of this, we studied the citation disciplinary structures of China and Brazil in more detail. Figure 2 displays the R_Cij1993 and R_Cij2013 values across fields for Brazil and China.

For 1993 publications, Brazil’s citation impact in Mathematics, Space Science and Physics are relatively strong, whereas the performance in Biology and Medicine is relatively poor. For 2013 publications, however, Agricultural Sciences exhibits the (by far) strongest performance, with a large increase in world share compared to 1993. Besides, the corresponding shares for Biology, Environment/Ecology and Medicine have also increased a lot. For instance, the values for Environment/ Ecology are 0.4% (1993) and 1.5% (2013).

Regarding China, several fields show quite remarkable increases in world shares, especially Chemistry and Engineering. The world shares of Chemistry and Engineering increased with more than 20 percentage units from 1993 to 2013, while the shares for Biology and Medicine only increased with less than 10 percentage points. The findings indicate that the enormous upsurge of publications in the 20 years of our observation period hardly had an impact on the citation structure of the countries under analysis. The upsurge resulted in an absolute upgrade of the numbers of citations, but the disciplinary profiles are rather stable, even in transition countries like Brazil or China. However, there are changes in the profiles as the example of China shows. While the basic research fields of mathematics and physics were the largest in terms of citations in the Chinese profile at the beginning of the 1990s, they shifted towards the more application oriented fields of engineering and also chemistry (including material sciences). These changes, however, have a measurable but limited impact on the overall citation profile. There is more stability than change in the system.

Jeffreys-Matusita distances between publication and citation disciplinary structure within G7 and BRICS countries and in year 2013 are reported in Table 5. Also reported are the means of the elements of corresponding vectors, which are the world shares of publication volume and citations.

Table 5

Jeffreys-Matusita distances between publication and citation disciplinary structure and vector means within G7 and BRICS countries.

Most G7 countries, with United States as an exception, have lower values on the Jeffreys-Matusita distance than BRICS countries, indicating a higher degree of heterogeneity between the publication and the citation disciplinary structure for the latter countries. The distance for United States is much higher compared to the other G7 countries, which indicates a substantial difference between the two types of disciplinary structures.

For the G7 countries except Japan, Mean(V_Ci2013) is larger than Mean(V_Pi2013), which indicates that on average across the fields, the citation impact performance is stronger than publication volume performance. This result is particularly striking for USA, with Mean(V_Ci2013) equal to 25.3, much higher than Mean(V_Pi2013) (19.2), and with the largest Jeffreys-Matusita distance of 2.1, indicating that USA gets much more citation impact with fewer publications. For the BRICS countries and Japan,Mean(V_Ci2013) is less than Mean(V_Pi2013): The citation impact of these countries lags behind publication volume. This is the case especially for Russia. Mean(V_Ci2013) (1.09) is considerably smaller than Mean(V_Pi2013)(2.58), which indicates that Russia has less impact with more publications.