Tracing the evolution of physics with a keyword co-occurrence network

We apply our method to seven physics fields, which are selected based on the KPS report to describe the evolution of emerging academic fields. Target physics fields and their initial keywords are listed in Table 1. We have two fields that have single initial keywords. Other fields have multiple keywords since they have multiple keywords expressing their fields. Using these keywords, we collect publications and build a keyword co-occurrence network.

The basic statistics of the publications and generated networks are also summarized in Table 1. We collect more than 20,000 publications except for the origin of the universe field. The number of publications in the origin of the universe field is small because our dataset covers only publications in the physics field, not in the astronomy field of WoS. Because of this, the network would explain the structure in the physics field. We also see that about 99% of keywords are excluded when we construct the network. It means most of the keywords appear less than 5 times with other keywords. For the remaining keywords, we find communities and core keywords with high centrality.

The network structures of complex system, quantum matter, and the origin of the universe field are presented in Figure 2. And the networks of the rest four fields are described in Figure 3. We denoted the community structure and significant nodes in the network. For example, in Figure 2(a), the two keywords chaos and synchronization consist of large communities and have high centrality values. One interesting point about core keywords is that initial keywords rarely appear as the core keywords. Due to the method to expand the keywords set, we can exhibit other relevant keywords rather than initial keywords.

The communities in the network are shown with the color in Figure 2. We can find 7 to 10 communities, and each community represents a subdiscipline of the target field. We can infer the characteristics of the subdiscipline by observing keywords and their connecting keywords. Some nodes are connected with a large number of other keywords, such as nanoparticle, quantum dot, and solar cell (Figure 3(a-b,d)). These connecting keywords are materials like SiO₂, which implicates that these communities are dealing with various molecules and materials as their research works.

In addition to this, we can find the difference between the two communities by observing the keywords. For example, in Figure 2(c), we can find two communities related to dark matter. One contains neutrinos, cosmic rays, and dark energy, while the other contains dark matter theory and dark matter simulation. Although the two communities are related to dark matter, we can infer that the first community is dealing with components while the second community is related to the theoretical approach. In summary, by observing the keywords and their connections, we can classify the characteristics of the subdiscipline and compare the difference between subdisciplines.

Then, does the keyword network map the structure of the target field? We observe complex system and the origin of universe network to check the details of the field. First, keywords in the field of complex systems are clustered by 7 communities (Figure 2(a)). The main communities are nonlinear dynamics and information theory, which are studied theoretically in the complex system field. Keywords in these communities are chaos, synchronization, nonlinear dynamics, entropy, mutual information, and etc. These keywords are the concepts that use in the complex system. Other communities are the applications that are studied recently in the complex system field. For example, econophysics is connected with nonlinear dynamics, entropy, and complex network. These communities have weak connections with theoretical subfields. The last community is a neural network, which is a recently emerging field. Several interdisciplinary researches have been done in this field.

For another example, the keywords for the study of the origin of the universe are clustered by 9 communities (Figure 2(c)). Different from the complex system, we can see that some communities are located closely, although they belong to different communities. These communities are aggregated to two main fields: particle physics and cosmology. The community of particle physics consists of ADS-CFT correspondence, M-theory, black hole, and super-symmetry. Another one is a community of cosmology, which consists of dark matter theory, modified gravity, inflation, and search for dark matter and energy. In the middle of these two fields, there is a community that connects two large communities. Cosmology of theories beyond the standard model and black hole has many links to both, implying that these keywords play a crucial role to connect fields.

In summary, the keyword co-occurrence network can provide three aspects of the target field. First, the community shows which research works have been done in this field, and the keywords describe the community. Second, the target network can be described with a proper value of the parameter. The community detection method provides a resolution parameterBlondel08JSMTE , which controls the size and number of the communities in the network. Although there exists an optimal parameter to divide the network, a proper level of the parameter can describe the description of the target field. Last, links between communities provide a clue to the evolution of the target field. As seen in Figure 2(c), there exists a community that connects two different fields, by observing a large number of links from the two fields. However, it does not imply a causal relationship or evolution directly.

As the keyword network provides limited information about the evolution of the target field, we check the change of keywords in time to capture the evolution. Above the seven fields, we display the complex system field to observe this change. We construct the keyword network from the publications of three years time window and two years moving window. In detail, we construct a keyword network for a year $y$ with publications till year $y+2$ and next construct the keyword network for a year $y+2$. We adopt a three-year time window to reduce the fluctuation of keywords and a two-year moving window to avoid publication overlap between the two networks. We repeat the process to generate communities as described in section III.1

After constructing the keyword networks, we find the flow of communities within two networks. To classify the most relevant communities, we compute similarity. If a community’s keywords in year $y$ mostly appear in a community in year $y+2$, we consider the two communities are most relevant. It can be described as $S_{ij}=|K_{i}\cap K_{j}|/|K_{i}\cup K_{j}|$ for the keyword set $K$ in the target community $i$ in year $y$ and community $j$ in year $y+2$. The equation is equivalent to the Jaccard similarity between two communities. In the case that the similarity $S_{ij}$ is the highest for community $i$, we consider that the community maintains its research subfield in the target field by time. Additionally, we can set a threshold $\delta$ so that the two communities are similar if $S_{ij}\geq\delta$. In this case, we can observe the merge and split of a community. In this work, we set $\delta=0.1$.

The flow of communities in the complex system field is described in Figure 4(a). The keyword mostly appears in the community, and the flow is the shared keywords between two communities. Starting from 2011, three communities of complex networks, entropy, and chaos keep remaining in the largest communities for all periods. These communities are also the largest in Figure 2(a), supporting that these communities are the main subfields in the complex system field for all periods.

However, two significant changes appear. First, the complex network community separates into the communities of phase transition and complex network. Phase transition community becomes the largest community after the appearance and changes in the molecular dynamics community. Phase transition is an important field in statistical physics, and it becomes a large community in the complex system field as it combines with molecular dynamics. The complex network field emerges in the late 1990s, and phase transition is also studied in the complex network field.

Second, the dominant keyword is changed in the chaos community. Chaos is the most appeared keyword in 2011 and 2013, but the number of appearances is decreased. In 2015, a keyword network has become the dominant keyword in the community. Note that the keyword network is different from complex network. It does not have any connection to the other keywords of complex network. The change of chaos community is described in Figure 4(b) and (c). It shows that the number of the appearance of keywords nonlinear dynamics and synchronization is increasing, while chaos is decreasing. It means that although the research subfield keeps a remaining position in the target field, the detailed work is slightly changing over time. These changes, however, are not directly traced in Figure 2(a). It only shows the big community of chaos. We also see that the increase of nonlinear dynamics and synchronization is also related to the increment of the network.

We also see the other minor communities in Figure 4(a). These communities are merged into and split from the large community. Communities can be minor research subfields in the complex system field, or they are just a new concept and an application of existing research works. Some communities are new concepts that arose from the existing research subfields so that they are merged into the largest community. And some communities are applications of the existing subfields so that they split from the largest community.