Insight into the Disciplinary Structure of Nanoscience & Nanotechnology

Disciplinary co-occurrence matrix reports the relationship among different disciplines of N&N, as operationalized as WCs. The matrix construction is the basic work for analyzing disciplinary network structure and disciplinary cliques here. WCs provide an effective level of measurement of discipline for the study of interdisciplinary processes (National Academies Committee on Facilitating Interdisciplinary Research, 2005). The 225 or so WCs (the number is adjusted slightly over time) reflect sub-disciplines (e.g. Organic Chemistry). WCs have been selected to map science disciplines (Leydesdorff, Carley, & Rafols, 2013), and to do many other bibliometric analyses (Fu & Ho, 2015; Garner, Porter, & Newman, 2014; Lin & Ho, 2015).

An article may involve contributions from two or more disciplines. Keep in mind that the classification into WCs is based on the journal of publication, not on analysis of the individual article. In the SCI-E database, some 40% of journals are associated with multiple WCs; for example, there are six WCs in the following article in the area of N&N.

TI: Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology

Chemistry, Multidisciplinary;

These six WCs in this record (this is an extreme example; recall that nearly 60% of journals are associated with a single WC) represent the co-occurrence relationship. That is, the record is associated with multiple disciplines (WCs). Bibexcel (Persson & Dastidar, 2013) and Ucinet (Borgatti & Everett, 1999; Freeman, Borgatti, & White, 1991) are jointly employed to get the WC co-occurrence matrix as follows (Table 1). Take the cell crossed by 5 and 8 with value of 1,794 for an example, it means that the co-occurrence frequencies of 5 (Chemistry_Applied) and 8 (Chemistry_Physical) are 1,794 times.

Table 1

Web of Science category, WC co-occurrence matrix (Partial).

After obtaining the WC co-occurrence matrix, we can map the disciplinary network by employing Netdraw (Johnson et al., 2009). The WC co-occurrence matrix we used here is the original matrix derived from the bibliographic data, and the Jaccard index method proposed by Leydesdorff (2008) has not been employed here, for the total disciplines (WCs) concerning N&N are not more than 40, and the disciplinary network structure can be visualized clearly by mapping directly from the original WC co-occurrence matrix. The disciplinary networks help us identify the ties among disciplines engaged in N&N and the evolution of the disciplinary network structure over time. It is simple for us to find out which disciplines have connections with a specific discipline in the network (Figure 2).

Figure 2

The indicator of betweenness centrality (Equation 1) is applied to measure each discipline’s mediating effect according to the path of Network-Centrality-Freeman Betweenness-Node Betweenness, embedded in the Ucinet program, and to further help us understand the mechanism of the evolution of N&N. Betweenness is a centrality measure of a vertex within a graph. Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes (Freeman, 1977).

If g_jk denotes the number of geodesics between j and k, the probability is 1/g_jk when all the geodesics are equally selected to be the communicative paths among each node. g_jk(n_i) represents the number of geodesics between two nodes including n_i and the betweenness centrality of n_i can be calculated by Equation (1): CB=∑<!-- ? -->j<<!-- ? -->kgjk(ni)/gjk.$$ \begin{array}{} \displaystyle C_B=\sum\limits_{j \lt k}g_{jk}\,\big(n_i\big)\,/\,g_{jk}. \end{array} $$(1)

The higher the betweenness centrality of a specific discipline concerning N&N is, the more contribution this discipline has made to the development of N&N.

Cliques analysis embedded in the Ucinet program is employed to do the disciplinary cluster analysis in the study according to the path of “Network- Subgroup-Cliques.” Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Since the numbers of disciplines concerning N&N are comparatively limited (no more than 40), and the disciplinary network is composed of a whole component, cliques analysis is found out doing well in a subgroup, and cluster analysis is found after exploring several other schemes (e.g. N-Clan, K-Plex, Lambda Set, Factions, f-Groups, etc.).

The disciplinary network structure of N&N, mapped by employing the social network analysis tool, helps us better understand the dynamic evolution of N&N over time from the perspective of the evolution of the network structure, such as nodes and links added over time. Tree diagrams of N&N disciplines inform the dynamic evolution of N&N from a logical view by showing relationships among different disciplines near or far.

In this technology’s early development phase (1981–1999), there are a total of 22 WCs participating in the N&N related disciplinary network (Figure 3), and these WCs are connected with each other, forming a whole network.

Figure 3

The map of the disciplinary network of Stage II, 1981–1999, in Figure 3 seems very dense, and the disciplinary network structure appears to be comparatively obvious, with concentrations relating to Nano-Biotechnology, Nano-Manufacturing, Nano-Materials, Nano-Electronics, Nano-Physics, Nano-Chemistry, Nano-Biomedical, and Nano-Thermodynamics.

In Figure 3, not only can we easily identify those WCs connected with N&N directly or indirectly but also determine if those WCs are also linked to any specific discipline (WC) directly or indirectly. In fact, each WC in Figure 3 can be mapped as an ego-network of disciplinary structure, as shown in Figure 2.

In Figure 3, the relationships among Physics Applied, Engineering Electrical & Electronic, and Nanoscience & Nanotechnology are the strongest ones in the network; the links among Materials Science Multidisciplinary, Metallurgy & Metallurgical Engineering, and Nanoscience & Nanotechnology are much stronger than the rest.

In Stage II, during 1981–1999, a total of seven WCs have played mediating effects (Table 2). The discipline of Nanoscience & Nanotechnology plays the highest mediating effect, with a normalized betweenness centrality of 68.095; the discipline of Physics Applied has the second highest nbetweenness centrality

nBetweenness refers to normalized betweenness centrality.

Table 2

Values of betweenness and nbetweenness centrality over 0 of each discipline in Stage II: 1981–1999.

In Stage III, the fast development phase from 2000 to 2014, more disciplines are added into the disciplinary network (Figure 4). The core N&N network expands to 34 WCs. These WCs are connected with each other, forming a whole network.

Figure 4

The density of the disciplinary network in Stage III is much higher than that of Stage II, especially the left part of the network. 12 new WCs are added in Figure 4 compared to Figure 3; they are Biochemical Research Methods, Chemistry Inorganic & Nuclear, Computer Science-Hardware & Architecture, Environmental Sciences, Materials Science-Biomaterials, Medicine-Research & Experimental, Multidisciplinary Sciences, Pharmacology & Pharmacy, Physics- Atomic-Molecular & Chemical, Physics-Fluids & Plasmas, Polymer Science, and Toxicology. A total of 14 WCs have played mediating effects in Stage III: 2000–2014 (Table 3).

Table 3

Values of betweenness and nbetweenness centrality over 0 of each discipline in Stage III: 2000–2014.

It is notable that Material Science Multidisciplinary plays a very important role with a much higher nbetweenness value than the other WCs—except for Nanoscience & Nanotechnology. It becomes a critical mediating point bridging other disciplines. In Stage III, the discipline of Nanoscience & Nanotechnology still plays the highest mediating effect with an nbetweenness centrality of 74.779; Materials Science Multidisciplinary has an nbetweenness centrality of 6.629; there are two other disciplines with an nbetweenness value exceeding 1.0—Physics Applied with 1.705 and Chemistry Multidisciplinary with 1.231.

In order to have an overview of the two development stages, Stage II and Stage III, three indicators (density, average distance, and mean nbetweenness (m-nbetweenness)) are selected to do the comparison, and the results are shown in Table 4.

Table 4

Comparison between two stages: Density, avg. distance, and m-nbetweenness.

Table 4 shows that the value of density is higher in Stage III than in Stage II, indicating closer relationships among N&N related disciplines over time. As far as average distance is concerned, the average distance becomes further as time goes on, which is mainly due to more and more subjects that have appeared. In terms of mean nbetweenness, the value is smaller over time, which is also because of more WCs participating in the arena of N&N over time.

According to the method illustrated in Section 2.2, and following the path of Network-Subgroup-Cliques of Ucinet, selecting tree diagram as the diagram type, nine cliques (Figure 5) have been found in Stage II, the preliminary development phase (1981–1999), as follows.

Figure 5

Chemistry Multidisciplinary, Chemistry Physical Materials Science Multidisciplinary, Nanoscience & Nanotechnology, Physics Applied, Physics Condensed Matter

Figure 5 shows that the cliques of N&N are clearly identified in Stage II: 1981–1999. There are six branches from the root in the tree diagram, and they are (1) Nano-Biomedical, Nano-Biotechnology, (2) Nano-Metallurgy, (3) Nano-Manufacturing, (4) Nano-Material, (5) Nano-Mechanical, and (6) Nano-Thermodynamics. This indicates that in this phase, many branches of N&N have come into being. The linking branch with Nano-Material is the biggest one in the map associated with some other sub-branches, such as Nano-Chemistry, Nano-Electronic, Nano-Physics, and Nano-Optics.

By using the same method, we get 18 cliques (Figure 6) in Stage III, the fast development phase, 2000–2014, as follows.

Figure 6

Chemistry Multidisciplinary, Chemistry Physical, Materials Science Multidisciplinary, Nanoscience & Nanotechnology, Physics Applied, Physics Condensed Matter

Figure 6 demonstrates two imbalanced domains of N&N: A smaller one is about Nano-Biomedical/Pharmacy; the much bigger one is covering Nano-Manufacturing, Nano-Metallurgy, Nano-Electronic, Nano-Mechanics, Nano-Biotechnology, Nano-Chemistry Analytical, Nano-Electrochemistry, Nano-Biochemical, Nano-Environmental Science, Nano-Chemistry Physical, Nano-Chemistry Applied,Nano-Optics, Nano-Materials, Nano-Physics, Nano-Mechanical, Nano-Thermodynamics, and Nano-Toxicology.