## 3 Methods and Materials
### Authors' Network  
This section presents the author network, which consists of the authors as the nodes and the edges between them as reflections of their predicted co-collaboration, while the weight of the edge represents the degree of their similarities. Additionally, the authors have been clustered based on their research area, including the expert author in each area, which are the individuals with the highest topic weight. In order to construct the collaborative academic network, we built an undirected weighted graph reflecting the predicted degree of collaboration based on their similarity. This is given that \(\text{G}=\ (\text{V},\text{E})\), wherein \(\text{V}\) represents the vertex (node) for each author in the network \((\text{v}_{\text{i}}\in\text{V})\), while the edge \((\text{e}_{\text{ij}}\in\text{E})\) is the evidence of the degree of similarity between two authors' nodes \(\left(\text{v}_{\text{i}}\text{ and v}_{\text{j}}\right)\). While the edge \((\text{e}_{\text{ij}})\) and weight \((\text{w}_{\text{ij}})\) reflect the number of their similarities  
Furthermore, a threshold set-up was applied to the edge values to remove the influence of insignificant probabilities on similarity edges between author nodes, meaning they will not add noise to the similarity calculation; this threshold was set to neglect all probabilities below 67%. Additionally, useful features were also added to the network; when a node is hovered over or clicked on, a new window appears containing specific information about that author. This includes the following elements:  
* Their total number of published papers;
* Their total number of citations;
* The range of their publication years;
* Their main field of study;
* The name of their university;
* A ranked list of similar authors' names and their similarity percentages. The process for building the authors' network is shown in Algorithm A4 (Appendix A). In order to cluster the authors based on their main research area, they are represented according to the highest topic weight in the topic's distribution for each of them (lines 5-10). Moreover, a node has been added in the graph for each author; its color should correspond to the author's research area, while there is an increase in the size of the node in order to represent the expert in that topic (lines 11-19). Lastly, edges have been added between the authors if their similarity is higher than 66% (lines 20-28). Additionally, when the node is clicked on or hovered over, all edges connected to that node are displayed as thicker edge lines in a color that highlights to distinguish them from others; this allows for the easy identification of directly connected nodes. Hovering the cursor around an edge also shows the similarity percentage of all connected nodes. Algorithm A5 (Appendix A) illustrates the steps taken to rank the authors' similarity list, while Figure 8 offers a representation of the proposed interactive network visualization. Figure 7: Assigning process for the author’s main research area. The link analysis uses two measurements: relatedness and significance. However, the relationship between two nodes in the same graph is measured in accordance with their relatedness. Subsequently, after building the network graph with a threshold of the edges, to evaluate the importance of a node in the network, the PageRank algorithm was implemented. It was introduced originally by Google Search during the process of grading websites in their search engine results in order to rank pages that have been indexed by a search engine. Furthermore, it measures the likelihood that a person that will arrive at any particular page [31]. In relation to this, we implemented the PageRank on the authors' network, yet as it is an undirected graph, we converted it into a directed graph by only adding another edge between two nodes if there was an originally existing undirected edge \((\mathrm{e_{i}},\ \mathrm{e_{j}})\). Hence, one edge will be pointing into (in) \(\mathrm{v_{i}}\) and the other out of (out) \(\mathrm{v_{j}}\).