# Corner Centrality of Nodes in Multilayer Networks: A Case Study in the Network Analysis of Keywords
## 3 Experimentation
### Experiment 3: Author Keywords vs. KeyWords plus Keywords  
In this experiment, we wanted to obtain the corner centrality value of a set of author keywords using the relationship with the KeyWords Plus keywords from Web of Knowledge. Typically, authors select keywords, so we will call these words \"author keywords\". However, it is more likely that authors do not have the freedom to choose keywords and automatic algorithms, and so predefined categories are used instead [29]. KeyWords Plus is one such alternative to author keywords. KeyWords Plus keywords are automatically generated from the titles of the articles that are referenced in a paper. According to [30], KeyWords Plus tries to reduce the problems generated by letting authors select their own keywords. In the same way as Experiment 2, we obtained a set of author keywords from a corpus of 69,000 documents as a result of a search in Web of Science, using \"Computer Science\" as the search criteria but without applying any filters to the documents, either for type or area, to obtain the academic literature that discusses computer science but is not limited exclusively to this area. The set of author's keywords was composed of 48,115 words, and the set of KeyWords Plus keywords contained 24,040 words. In this multilayer network, we had two layers. The first layer was composed of the author keywords as nodes, and between the nodes, a link existed if they appeared in the same paper. The initial importance of the nodes was the number of papers in which the author keywords appeared. In the second layer, the nodes were the KeyWords Plus keywords. Similarly to the other experiments, the nodes had an initial importance equal to the number of papers where they appeared. In this second layer, two nodes were connected if they were in the same paper. Additionally, between nodes in layer 1 (author keywords) and nodes in the second layer (KeyWords Plus), a link could exist if they shared the same  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Nodes**} & **Spearman’s Correlation** & **Rank-Order** & \multicolumn{2}{c}{_p-Value_} \\ \cline{2-5}  & **Mean** & **Std** & **Mean** & **Std** \\ \hline
100 & 0.604 & 0.065 & 0.000 & 0.000 \\
150 & 0.691 & 0.041 & 0.000 & 0.000 \\
200 & 0.683 & 0.039 & 0.000 & 0.000 \\
250 & 0.673 & 0.036 & 0.000 & 0.0  
paper. Our aim in this multilayer was to obtain the corner centrality value of the set of author keywords. In this case, an author keyword would have a higher centrality if the relative importance was higher in the layer of author keywords and the layer of KeyWords Plus keywords. In Figure 5a, the 50 authors' keywords that appeared in the highest number of papers are presented. Moreover, the 50 author's keywords with the highest corner centrality are on Figure 5b. In these word clouds, the size of the word is related to the value given. Therefore, the ranking given by corner centrality distinguishes between the words with high importance, such as education (first place), machine learning (second place), and computer science (third place). Likewise, we obtained the KeyWords Plus keywords with the highest centrality and compared them with the KeyWords Plus keywords most frequently used in the papers. Thus, in Figure 6a, the 50 KeyWords Plus keywords with the highest frequency are shown, and on Figure 6b, the 50 KeyWords Plus keywords with the highest values of corner centrality are shown. Figure 5: Two word clouds that compare results of the corner centrality value with the 50 most frequent keywords. (**a**): The 50 author keywords with the highest frequency. (**b**): The 50 author keywords with the highest corner centrality value. Figure 6: Two word clouds that compare results of the corner centrality value with the 50 most frequent keywords. (**a**): The 50 KeyWords Plus keywords with the highest frequency. (**b**): The 50 Keywords Plus keywords with the highest corner centrality value. Validation  
To validate the corner centrality measure, we compared it with the Pagerank versatility method [26].