## 4 Case Study: Citation Network Analysis Using ACL Data Corpus
### Dataset and Method  
We used the ACL ARC citation network data comprised of 318,351 citations instances (edges) and 86,825 papers (nodes) that make a citation network between publications in the ACL Anthology and outside the ACL Anthology with canonicalized IDs [22]. ACL dataset is freely available online along, with their full-text and citation networks. Therefore, we used this dataset. We further deployed our trained CNN-based citation classification model to automatically classify these citations links into binary class (important and non-important) and multi-class (use, extend, compare or contrast, motivation, background, future) citation functions. We used the state-of-the-art graph visualization open-source software Gephi [56] to analyze many elements of the citation graph created by the ACL ARC citations dataset between publications from ACL and outside the ACL. Furthermore, we utilized the multiple properties of the graphs, Table 2 presents the abbreviations and the details of the used algorithms:  
In addition to the quantitative indicators mentioned in Table 2, we highlighted the edges between the nodes (papers) to illustrate the interaction among ACL ARC papers with respect to their citation behaviors, both for binary and multi-class citation functions. Each edge is highlighted by a different color to represent the different citation behaviors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measure** & **Abbreviation** & **Description** \\ \hline Average degree & AD & The average degree of a graph in a citation network is defined as the average number of citations or edges a node has with other nodes [57]. \\ \hline The weighted average degree & WAD & It is determined from the average number of connections that a node in a network has with another node, where weight is generally specified as the total number of edges for a given node [57]. \\ \hline Graph density & GD & A graph is said to be complete if every node is connected to every other node by an edge. This property is taken into account by graph density, which counts the number of edges in a graph to determine how close a graph is to completion. \\ \hline Modularity & Mod. & In a graph, modularity is a measure of the strength of nodes that develop modules or clusters in the network. A highly connected group of nodes gives a high modularity value; yet, these groups of nodes may have sparsely interconnected connections [58]. \\ \hline Connected component & CComp. & A connected component (CComp) is a sub-graph of an undirected graph with a path connecting every other node in that sub-graph [59]. \\ \hline Clustering Coefficient & CCoef. & The clustering coefficient is a measure of how well all of the nodes in a network cluster together [60]. \\ \hline Average path length & APL & The longest path between two nodes in a network is referred to as path length. It is worth noting that the Average path length gives the perception of information diffusion in a network [61]. \\ \hline Eigenvector centrality & EC & According to [PERSON] [62], Eigenvector Centrality is the measure of influence that a particular node holds in a network based on its number of connections. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Network-level properties along with their abbreviations and descriptions. Overall, we examined our citation network in terms of three aspects: (a) we offered a variety of quantitative metrics to visualize the overall trend of ACL ARC data; (b) we displayed networks of selected papers to demonstrate the community interactions; (c) we illustrated the citation edges on the basis of their citation function using the top 1% nodes with respect to their node degree. Table 3 presents the network level properties of the citations network using complete ACL citations data and the top 1% of the total nodes. ACL ARC data forms a dense network (nodes: 86,825, edges: 318,351), with an average degree greater than 15 and a modularity value of 0.609.