## 5 Results: Quantitative Analysis and Most Important Publications
### Collaboration Analysis  
This section presents an analysis of collaboration networks, both in terms of collaborations between affiliations and countries. This study is conducted for both the _All_ dataset and its partitions \(All_{Early}\), \(All_{Medium}\), and \(All_{New}\), as well as for the _Review_ dataset and its partitions \(Review_{Early}\), \(Review_{Medium}\), and \(Review_{New}\). Table 6 shows the characteristics of the collaboration networks between affiliations (\(ACN\_i\)) in the first four rows and those of the collaboration networks between countries (\(ACN\_i\)) for the _All_ dataset. For each network, the table reports the network size in terms of node and edge cardinality (\(|V|\) and \(|E|\), respectively), the maximum and average degree values (maxD and \(\overline{D}\), respectively), the maximum and average weighted degree values (maxWD and \(\overline{WD}\), respectively), the average ratio between degree and weighted degree \(\overline{D/WD}\), and the network density. As expected, the size of the collaboration networks is significantly larger than that of the country-level collaboration networks, although the latter exhibit much higher density \(\rho\). The networks show similar maxD values, whereas \(\overline{D}\) values are much higher in country-level collaboration networks. Regarding weighted degree, both the maximum and average values are much higher in the country-level collaboration networks. Finally, the \(\overline{D/WD}\) ratio is higher in affiliation-level collaboration networks. Overall, the highest collaboration values are consistently observed in the most recent periods. Table 7 shows, in the first part, the affiliations with the maximum degree and, in the second part, the countries with the maximum degree in each network. This indicates the affiliations (or countries) with the highest number of connected affiliations (or countries) as collaborators. The third column lists those with the maximum weighted degree (WDegree), representing the entities with the highest total number of collaborations. MaxDegree and MaxWDegree can differ significantly. For example, an affiliation (or country) may have one collaborator with whom it has a high number of interactions, while simultaneously having many collaborators with whom it has few connections. \begin{table}
\begin{tabular}{l l r r r r r r r r} \hline \hline  & **Network** & \(|V|\) & \(|E|\) & \(maxD\) & \(\overline{D}\) & \(maxWD\) & \(\overline{WD}\) & \(\overline{(D/WD)}\) & \(\rho\) \\ \hline \multirow{4}{*}{_Category_} & \(ACN_{all}\) & 38,423 & 73,135 & 132 & 3.81 & 138.00 & 3.94 & 0.89 & 0.0001 \\  & \(ACN_{early}\) & 12,125 & 18,399 & 57 & 3.03 & 112.00 & 3.23 & 0.85 & 0.0003 \\  & \(ACN_{medium}\) & 7724 & 12,623 & 44 & 3.27 & 54.00 & 3.33 & 0.89 & 0.0004 \\  & \(ACN_{new}\) & 18,994 & 42,214 & 119 & 4.44 & 123.00 & 4.56 & 0.91 & 0.0002 \\ \hline \multirow{4}{*}{_Category_} & \(NCN_{all}\) & 150 & 1749 & 99 & 23.32 & 1556.00 & 89.65 & 0.60 & 0.1565 \\  & \(NCN_{early}\) & 107 & 563 & 57 & 10.52 & 326.00 & 23.85 & 0.67 & 0.0993 \\ \cline{1-1}  & \(NCN_{medium}\) & 109 & 492 & 52 & 9.03 & 212.00 & 18.39 & 0.70 & 0.0836 \\ \cline{1-1}  & \(NCN_{new}\) & 138 & 1445 & 88 & 20.94 & 1018.00 & 64.43 & 0.63 & 0.1529 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Affiliation collaboration network (ACN) and nationalities collaboration network (NCN) characteristics. Tables 8 present the main characteristics of the ACN and NCN networks built on the _Review_ dataset. As in the case of _All_, the tables are organized into two sections: the first four rows provide information regarding the collaboration networks among affiliations (ACN), while the subsequent four rows contain information about the collaboration networks among countries (NCN). The network size (\(|V|\) and \(|E|\)) grows significantly in the most recent period. The network density is higher in the early and intermediate periods compared to the entire period and the most recent period.