Coevolution of theoretical and applied research: a case study of graphene research by temporal and geographic analysis

As an emerging field, science of science (SciSci) has attracted a great deal attention recently (Zeng et al., 2017; Fortunato et al., 2018; Wang and Barabási, 2021). In SciSci, science is treated as a complex system, which include ideas, papers, scientists, funding agencies and, more importantly, the connections among them. Using methods from complex system and complex network, researchers have revealed many interest findings of Science from data. They includes universal citation distribution (Radicchi et al., 2008), scientists’ career dynamics (Petersen et al., 2012), the role of team in science (Wuchty et al., 2007), just to name a few.

As a complex system, science ecosystem has obvious hierarchical structure: roughly speaking, science includes physical science and life science, physical science includes physics, astronomy, chemistry and earth science, physics includes mechanics, electromagnetism, thermodynamics, relativity, quantum physics and so on, electromagnetism itself also have its internal fine structure. At each hierarchical level, scientific elements (people, ideas, papers) are closely connected within disciplines, and loosely connected between disciplines. These naturally exist modular structure provide convenience to SciSci research since we can concentrate on particular discipline by assuming the influence from other disciplines is negligible. This kind of discipline level analysis not only give insight of one particular field but also shed light on general principles of scientific enterprise. Therefore, people’s interest on discipline analysis has been growing rapidly.

One of the earliest extensive studies on this subject was done by Bettencourt and Kaur (2011). The authors focus on the evolution of sustainability science, a new discipline emerged in 1980s. By analyzing a large corpus of relevant publications, they found that sustainability science has been growing explosively since its advent in the 1980s. This discipline has an unusual spatial distribution of its contributions: they are widely distributed in both developed counties and developing countries; the collaboration network has strong roots in national capital rather than traditionally more academic cities. To capture the main themes that define the filed, the authors decomposed the corpus into traditional disciplines and found they are integrated management of human, social, and ecological systems from an engineering and policy perspective. The work in Bettencourt and Kaur (2011) also revealed that the unification of sustainability science happened around the year 2000 by collaboration network analysis.

One recent discipline analysis look to artificial intelligence (AI) research (Frank et al., 2019). The authors tried to figure out whether AI research and relevant social science fields keep pace with each other. To answer this question, they used citation to track the communication between AI research and other fields. They analyzed citation flows from 1950 to 2018 and found these flow are neither constant nor symmetric. AI research cited philosophy, geography and art a lot in its early years, however current AI research cited mathematics and computer science most strongly. On the other hand, other fields didn’t cite AI research in proportion to its growing number of publications. There is an attention gap between AI research and social science.

Here, we conduct a discipline analysis of graphene research, a relatively young field focus on single layer of carbon atoms arranged in a two-dimensional honeycomb lattice. Since Novoselov et al. (2004) seminal work, which helps Andre Geim and Konstantin Novoselov won Nobel Prize in Physics in 2010, the interest in graphene has grown explosively and even led European Commission to fund Graphene Flagship with €1 billion budget (homepage, 2021a) and the creation of National Graphene Institute in UK (homepage, 2021b). Therefore, it is important and beneficial to understand graphene research as a emerging research discipline. It will not only increase our knowledge about scientific enterprise at discipline level, but also provide useful information of the whole discipline to PhD students, graphene scientists, universities and funding agencies.

Generally speaking, there are two reasons that attract people to do graphene research: 1) graphene is very strange from a theoretical perspective. It is the first example of two-dimensional atomic crystal and it was thought that such structure is thermodynamically unstable. The graphene’s electronic properties are peculiar: electrons behave as massless relativistic particles. 2) graphene is very attractive from an applied perspective. It has many properties which are better than those in all other materials. Hence, graphene has enormous potential to improve many applications, range from electronics to medicine. And these two reasons guide people go to different directions and form two branches: theoretical branch and applied branch. Although this division is well known in graphene research community, there is a lack of quantitative analysis from this perspective (Barth and Marx, 2008; Lv et al., 2011; Nguyen et al., 2020). To fill this gap, we collect graphene research literature and conduct a systematic analysis. First we identify these two branches by their word frequency, then validate the division result with keywords. We find that theoretical branch includes around one third of all papers and applied branch includes remaining two third. We check how these two branches developed temporally and geographically. The results show that yearly proportion of applied branches decreased from 2004 to 2007 and kept increasing since then. The research contribution mainly come from a few regions, and geographic distributions are quite different in theoretical and applied research. Finally we study the interaction between two branches and find theoretical research extremely relies on past theoretical research while applied research heavily relies on past applied research. Temporal analysis suggests that this self-dependence was very stable for theoretical research while grown significantly for applied research. And this trend holds for all main regions of graphene research.

This paper is organized as follows. In Sec. 2 we describe our dataset and the framework to quantify and analyze the inside coevolution. In Sec. 3 we present our main results, namely, the internal structure of graphene research and linguistic validation, spatial and temporal analysis of graphene publications and their interdependence, and also discuss the limitations and implications. Sec. 4 summarize our findings and suggests future perspectives.

We start our study by identifying theoretical and applied papers in our data collection. Given the complexity of research, this dichotomy may miss a little information since some papers are hard to be categorized. However, this classification is well accepted by graphene research community and our results are in good agreement with this convention. Dividing graphene literature into two branches can capture the most significant heterogeneity inside graphene research. Therefore, we use theoretical/applied dichotomy through this paper and call them T and A for short.

It is well known that word frequency changes significantly from field to field. We assume theoretical graphene papers tend to use a set of words frequently while applied graphene papers tend to use another set of words frequently and these two sets of words are distinct. Based on this assumption, we first counted all words in titles and abstracts of 115,988 papers through standard natural language processing techniques (tokenization, stopword filtering, stemming and so on). The words with frequency larger than 0.01% are selected as feature words and we have 12328 of them. Every article is represented by a 12328-dimensions vector $(a_{w_{1}},a_{w_{2}},\dots,a_{w_{12328}})$ and ${a_{w}}_{j}$ is the count of word $w_{j}$ in that article. Combining all paper vectors together, we constructed a $115988\times 12328$ paper-word matrix. Then the CoClus method in Sec. 2.2 was applied to extract no-overlapping clusters. In CoClus we must specified number of cluster $k$ first to find best partition with this $k$. Normally, the number of clusters is unknown at the beginning. The common protocol is to repeat this process with different $k$ and choosing $k$ with highest modularity as the result. We run CoClus algorithm with $2\leq k\leq 9$ and found the modularity peaks at two values $k=4$ and $k=6$, see supplementary information for more details.

However, the cluster structure in paper-word network is quite fuzzy. More effort is needed to get the reasonable partition. By comparing best partitions under different $k$, we noticed they share a common feature: one group repeatedly occurred in most partitions while other groups are not stable. It suggests that there exist a distinct boundary between that group and others while other detected structures are more or less the “overfitting”. To show the stability of this ”hyperstructure”, we compare the partitions with two highest modularity, namely, $k=4$ and $k=6$. In case of $k=4$, We named the stable group as I and other groups as II, III, IV for convenience. For the same reason, we named the stable group as 1 and other groups as 2, 3, 4, 5, 6 in case of $k=6$. Since the sum of group II, III and IV is the complement of group I, we call it group I’ and also call the sum of group 2, 3, 4, 5, 6 as group 1’. We find group I has 43323 papers, group 1 has 42798 papers and they have 40406 papers in common; group I’ has 72665 papers, group 1’ has 73190 papers and they have 70293 in common. The situations are very similar for other $k$ values. Therefore, to avoid the “overfitting”, we use the “hyperstructure” with $k=4$, namely group I and I’ as the partition result.

Using the keyword extraction method, we found the stable group is about theoretical research and we call it T. Other three groups under $k=4$ are (1) synthesis and functionalization, (2) supercapacitor, and (3) sensor. That also explain the fuzzy boundary between them since they are closer to each other than they are from theoretical research. Since they are application-oriented research comparing with T, we merged them into one cluster as A. There are 72665 papers, 8162 words in group A and 43323 papers, 4166 words in group T. We visualized the partition in Fig. 2: paper vectors in T are colored blue and paper vectors in A are colored red. We also sorted columns to make first 4166 columns represent words in group T and remaining 8162 columns represent words in group A. As illustrated by Fig. 2, it is apparent that first 4166 words are used more frequently in group T and other words are used more frequently in group A since these areas are darker than adjacent blocks. And this is exactly the aim of co-clustering: high in-cluster density and low cross-cluster density. It is worth noting that there are three subclusters inside A (these blocks are darker than other red area). They are more specific topics (1) synthesis and functionalization, (2) supercapacitor, and (3) sensor, respectively.

To validate the clustering result and have an intuitive picture of research topic, we built a keyword list for each cluster. To avoid statistical fluctuations, we only considered the words those are in top 2% sorted by frequency. The results are not sensitive to the quantile we chosen here as long as we dropped rare words (large fluctuations). These keywords are ranked by their z-scores and top 25 keywords for T and A are shown in Fig. 3. The lists are very informative: list A covers hot terms in applied graphene research, like electrochemical, cycles, supercapacitors, batteries, electrode, lithium and so on; list T covers key concepts in theoretical graphene research, such as Dirac, gap, spin, calculations, band, point, states and so on. Therefore, we can conclude confidentially that co-clustering method successfully divide graphene research literature into theoretical branch and applied branch. We also give two more extensive word clouds for T and A in SI.

Based on the co-clustering result, we first analyze the proportion of T and A. Among all graphene research papers, 62.6% belong to group A and 37.4% belong to group T. It suggests that graphene research attract attention from both theoretical and applied perspectives and both have made indispensable contribution to this field. Furthermore, this ratio is not constant over time. As shown in Fig. 4, the proportion of T increased from 70% to around 90% during 2004-2007, then gradually decreased to lower than 30% in 2017. (Our temporal analysis focus on papers since 2004 because that is the year graphene got global attention and papers about graphene before 2004 are rare, only about 0.5% in our dataset.) These curves indicate that at the early stage of graphene research, theoretical branch played a dominant role and gained even more popularity until 2007. After that applied branch grown relatively faster and became the majority after 2012 and this trend kept until 2017. The reason behinds this process is not clear. Our speculation is that after Novoselov et al. (2004) seminal paper, graphene research attract a great deal of attention. At that time, this area was still in it’s infancy and many theoretical questions remained to be answered, while preparation of graphene was difficult and expensive, applied research is only limited to few labs. So researchers published more theoretical papers than applied papers. As time elapsed, people gained more understanding of graphene, low-hanging fruit has been picked and theoretical questions became more difficult and time-consuming. On the contrary, technical advancement make preparation of graphene easier. It lowered research barrier and allowed more scientists joined the applied research. Also, more understanding of graphene inspires more application scenarios, which motivate more applied research. All of these factors together shape the curves in Fig. 4. Although this hypothesis remains to be validated, our finding that proportion of group A has increased steadily since 2007 provide a big picture of graphene research ecosystem for researchers, companies and funding agencies.

Beside temporal evolution, we also studied geographic distribution of graphene research. As a highly actively field with enormous economic potential, it attracts scientists and engineers all over the world. Affected by tradition, manpower and funding policy, regions may have different aims and preferences in graphene research. To validate this conjecture, we calculated regional credit using method in Sec. 2.4. By summing all papers’ credit distribution, we are able to measure each region’s contribution in the whole field. As shown in Fig. 5, Mainland China is the topmost player in both theoretical and applied research, with 22.4% share in T and 51.8% share in A. That means Mainland China’s contribution in applied research is even more than the sum of all other regions. The United States is also a big player with 18.9% share in T and 7.5% share in A. In contrast to Mainland China, US has more share in T than A. It suggests that Mainland China is more focus on applied graphene research while The United States takes a more balanced position. Furthermore, the composition of Fig. 5 (a) and (b) reveal a subtle difference between theoretical and applied research: there are 13 regions with at least 2% contribution in T while only 7 such regions in A. It suggests that applied research is less geographically diverse than theoretical research. The reason behinds is complicated, may due to economic factor, funding policy, research culture and so on. We leave it for future research.

So far we have studied the graphene research temporarily and geographically. If this two dimensions are combined together, we are able to analyze evolution of graphene research in particular regions. More concretely, for a given region in a given year we can calculate its credit in T ($C_{T}$) and A ($C_{A}$) by method in Sec. 2.4 using publications only in that year. Then the yearly proportion of T and A of that region in that year can be calculated as $\frac{C_{T}}{C_{T}+C_{A}}$ and $\frac{C_{A}}{C_{T}+C_{A}}$. And we plot yearly proportion of T/A for six regions in Fig. 6. These six regions have at least 2% share in both theoretical and applied research (see Fig. 5), therefore, are considered as top players in graphene research. The curves in Fig. 6 can be thought of as regional version or components of Fig. 4 and it shows that all six regions follow the same general trend in Fig. 4: gradually decrease of theoretical research and increase of applied research. However, that shift occurred slower in The United States than in other regions. It suggests that research community in The United States still put considerable resource in theoretical research. This finding is very important to understand graphene research competition among regions and make funding policy.

Like most, if not all, science research fields, both theoretical and applied branches are indispensable parts of graphene research. Each of them has its own mission and focus. At the same time, they both rely on the communication with each other: theoretical research gets feedback from applied research, applied research receives guideline from theoretical research. This inside coevolution is extremely important for any science research fields. If this coevolution mechanism does not work well, that research field will experience certain difficulty to move forward, like Aristotelian Physics or science in ancient non-western civilizations. Given such importance, we quantified the inside coevolution in graphene research in terms of interplay between T and A. The dependency factors were computed for all papers, then the average values were calculated for papers in group T and A respectively. As shown in Table 1, both T and A rely more on itself than others. However, the difference is obvious: T is critically depend on T (90%) while A is relatively rely on A (69%). This result illustrates a remarkable difference between T and A: theoretical research is mostly driven by other theoretical research, on the other hand applied research pays fairly high attention to theoretical research. On possible interpretation of this difference is that: theoretical graphene research have achieved significant progress and its current effort is beyond existing technology, while applied research benefits a lot from theoretical research and as the result A cites T, directly and indirectly, a lot. More evidences are need to verify this explanation, however, given the fact that in history of science theory is ahead of application at most of time , we believe it is a plausible explanation.

The numbers in Table 1 is aggregated results of papers published in all years. Even though they provides many insights for us, the temporal information is lost. To get a better understanding of coevolution process, we calculated the average values of T/A dependency for T/A papers in each year and plot them in Fig. 7. As shown in that figure, dependency curves behavior significantly different between theoretical and applied group: the curves in T is very stable, while the curves in A underwent dramatic changes during that time. From 2004 to 2006, A’s dependency on T increased from 0.3 to 0.7 and gradually decreased afterward. That is to say applied graphene research is mainly driven by theoretical research at early stage and become more motivated by it self as time goes on. This result suggests that the inside coevolution is not a “static equilibrium”, but rather a “dynamic process”. Not only proportions of T and A change with time (Fig. 4), the interaction between them also changes. More work is needed to fully understand the reason behind these changes, and our finding can serve as the basis for further research.

We have already shown the geographically difference in Fig. 6. Does such effect also happen in T/A dependency? To answer this questions, we grouped all papers according to authors’ affiliation region, and calculated their T/A dependency of T/A. We only consider papers with all authors in the same region since it is not clear to attribute dependency to regions with international collaborated papers. However, we found that single region papers are very similar to international collaborated papers in terms of dependency evolution. Therefore, the result here will not change much after international collaborated papers are included. Please see SI for more details. The results of topmost six regions are shown in Fig. 8. Unlike Fig. 6, all regions in Fig. 8 show roughly the same behavior, even for Mainland China and The United States. This suggests that the trend we found in Fig. 7 is a universal phenomenon for graphene research and is insensitive to geographic factor.

Discipline-level analysis give many insights of scientific enterprise, also offer important reference for practical purpose, like career decision, hiring decision, funding policy and so on. Some important works have been done with SciSci paradigm, for example the evolution of sustainability science, the structure and evolution of physics, and the development of artificial intelligence (Bettencourt and Kaur, 2011; Sinatra et al., 2015; Frank et al., 2019).

In this study, we complemented previous studies by investigating evolution of graphene research in terms of its main components: theoretical branch and applied branch. Using the co-clustering method we divided the graphene publication collection into two groups. By extracting each group’s keywords, we confirmed that one group is about theoretical research and the other does applied research. Overall, 37.4% of papers belong to T and remaining 62.6% are members of A. However, these ratios are not constants over time: the proportion of T increased to around 90% in 2007 and gradually decreased afterward, while the proportion of A did just opposite. It suggests that applied research grown faster than theoretical research and the attention of graphene research community shift gradually from theory to application. By analyzing authors’ affiliations, we computed region credit for every paper and all regions total contribution. The distribution of contribution is very different in T and A: many regions made significant contribution in T while Mainland China is dominant in A. And the evolution curves also show significant difference among regions. Using the dependency factor we invented, the reliance between theoretical research and applied research is quantified. We found that such dependency is asymmetric: theoretical research is extremely influenced by itself while applied research benefits from T and A in a more balanced way. Such dependency relation is very stable for theoretical research while changed significantly for applied research. And we found this phenomenon is insensitive to geographic factor, which suggests it is a universal process.

Although many interest findings were observed, several important questions remain to be answer. For instance, graphene papers were classified either as theoretical research or applied research in this study. However, this dichotomy may fail for some papers since collaboration between theorists and experimentists become common nowadays and it is inaccurate to put those paper either in T or A. In other words, an overlapping-clusters picture of graphene research may be a better description of reality . Future work should take overlapping into account given the importance of collaboration in modern scientific enterprise. In this study all graphene papers are treated with equal importance. This choice simplifies our analysis, but introduces deviation from reality: a few papers receive most attention. It would be beneficial to incorporate this fact into our framework and new results may give us a better picture of graphene research.

This research is supported by the Singapore Ministry of Education Academic Research Fund, under the grant number MOE2017-T2-2-075.

Conceived and designed the analysis: Wenyuan Liu.

Collected the data: Ai Linh Nguyen.

Performed the analysis: Ai Linh Nguyen.

Wrote the paper: Ai Linh Nguyen, Wenyuan Liu and Siew Ann Cheong

CN: Mainland China. US: The United States. JP: Japan. DE: Germany. KR: South Korea. IR: Iran. IN: India. RU: Russia. GB: The United Kingdom. FR: France. ES: Spain. IT: Italy. SG: Singapore. TW: Taiwan.