# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 8 ISN, ISN-AF and Baseline Comparisons
This ability of the proposed approaches is also confirmed by edge count, which is grater for ISN and ISN-AF with respect to the baseline approach. Moreover, the missing edges for the baseline involve a higher number of isolated connected components, which leads to higher CCC values. At the same time, the major incidence of sparse connected components reduces the giant component size, which is, in general, denoted by the \(root_{author}\) component. In fact, the GCS value for the baseline is 4.99%, while it reaches 6.65% for ISN and 6.90% for ISN-AF. As a practical example, to highlight the difference between the baseline and the proposed approaches, we report four retweet cascade graphs with increasing node sizes. The cascade trees are implemented using Gephi version 0.9.2 and the node size represent the number of node's descendent. In other words, the bigger the node, the higher is its importance for tweet propagation. Figure 7 reports the comparison of the retweet graphs generated by the three approaches with a total number of 67 nodes. While the baseline graph is characterized by a deeper tree with some sparse nodes, the proposed models' cascades (both ISN and ISN-AF) create a fully connected tree composed by only one level, since all the nodes are directly linked to the \(root_{author}\). Considering a bigger cascade, Figure 8 compares the three approaches when the retweet number is 106: this result visually explains the considerations about the higher number of isolated connected components created by the baseline algorithm. In fact, fromFigure 8c it is possible to observe the presence of numerous isolated connected components with nodes characterized by a valuable importance (node size) in terms of retweet propagation. It seems that the \(root\) has a minimum impact on the message propagation, while the other nodes (the big green and the big blue nodes) casually found the tweet and spread it. In contrast, the cascades in Figure 8a,b propose a different retweet path, giving more importance to the \(root\) and reducing also the number of single isolated nodes. In these two initial examples (Figures 7 and 8) the proposed methods are showing similar or identical behavior, which are substantially different from the baseline. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & **Edge Count** & **Depth** & **CCC** & **GCS (\%)** & **RFR (\%)** & **GRC (\%)** & **CAS (\%)** & **SNI(\%)** \\ \hline ISN (weight set 10) & 6.09 & 0.56 & 1.26 & 6.65 & 91.13 & 6.60 & 85.29 & 2.31 \\ ISN-AF (weight set 10) & 6.09 & 0.51 & 1.15 & 6.90 & 94.22 & 7.23 & 94.70 & 2.89 \\ Baseline & 5.49 & 0.37 & 2.25 & 4.99 & 92.23 & 6.32 & - & 6.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison between the two proposed approaches (with the best weight set) and the baseline approach. The other two examples (Figures 9 and 10) report cascades where ISN and ISN-AF produce different propagation paths. In this case, the retweet numbers are 1127 and 1180, respectively. For the baseline approach (Figures 9c and 10c) the node sizes, describing the nodes influence in the graph, favor the \(root\). Conversely, the proposed ISN model shows propagation paths that highlight the importance of non-root nodes in retweet propagation. For instance, Figure 9a shows the presence of important nodes (the big green and blue ones) that helped the propagation. These nodes are also present in the ISN-AF model (Figure 9b), but with a minor impact. A more visible difference between ISN and ISN-AF is apparent from Figure 10b. The number of nodes connected to the root according to the ISN-AF approach are 621, of which 538 links are derived by IS interactions and 21 by friend network analysis. Differently, Figure 10a reports the ISN-generated graph, which has 1146 nodes linked by timeline information, and is thus connected, adopting the IS metric.