# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 7 Evaluation of IS Weights
### Experimental Results on Cascades with at Least Five Nodes  
In terms of absolute CAS results, it is interesting to perform a more detailed analysis removing cascades with few nodes. Focusing on the graphs of the 90 th percentile, which are cascades with more than five retweets, Table 8 reports the average of the computed metrics. The first four rows report the results for the weight sets of the guideline setups. Set 0.0 achieved an average CAS of 47%, while cascades where the incidence of retweets was zero (set 0.1) achieved a CAS of 41%, with a slightly increased SNI (16.96% vs. 16.33% for set 0.0). This suggests that quotes and replies have higher impacts on CAS with respect to retweets. In fact for the sets 0.2 and 0.3, where the weights of quotes and replies were set to zero, the CAS value dropped to 38%, with an increased incidence of sparse nodes and a reduction in terms of GCS. When observing the first six experimental setups, which used the same three weight values \((0.0,0.3,0.6)\) assigned differently to the three interactions, the best CAS value was achieved by set number 4, where the priority was assigned to quotes, followed by retweets and replies. When observing the CAS distribution reported in the box plots in Figure 6a, it emerges that the highest median is related to set 6 followed by set 5. However, all the weights sets are characterized by similar distributions which tend to show positive asymmetry. In contrast, from the heatmap in Figure 6b, sets 5 and 6 are characterized by higher numbers of cascades, with CAS values above 0.5. Nonetheless, due to the retweet bias, our choice is to prefer weight sets in which the impact of retweets is minimal with respect to the other two interactions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{3}{c}{**Weight**} & \multicolumn{2}{c}{**CAS**} \\ \cline{2-5}  & **Set** & **Quotes** & **Replies** & **Mean** & **St Dev** \\ \hline \multirow{2}{*}{a} & 0.2 & 1.0 & 0.0 & 0.28 & 0.06 \\  & 0.3 & 0.0 & 1.0 & **0.32 \({}^{\star}\)** & **0.08 \({}^{\star}\)** \\ \multirow{2}{*}{b} & 1 & 0.3 & 0.6 & 0.26 & 0.07 \\  & 2 & 0.6 & 0.3 & 0.27 & 0.07 \\ \multirow{2}{*}{c} & 3 & 0.0 & 0.6 & 0.28 & 0.07 \\  & 4 & 0.6 & 0.0 & 0.30 \({}^{\star}\) & 0.08 \\ \multirow{2}{*}{d} & 5 & 0.0 & 0.3 & 0.29 & 0.07 \\  & 6 & 0.3 & 0.1 & 0.31 & 0.08 \\ \multirow{2}{*}{e} & 7 & 0.4 & 0.5 & 0.26 & 0.06 \\  & 8 & 0.5 & 0.4 & 0.26 & 0.06 \\ \multirow{2}{*}{f} & 9 & 0.3 & 0.5 & 0.28 & 0.09 \\  & 10 & 0.5 & 0.3 & 0.26 & **0.05** \\ \multirow{2}{*}{g} & 0 & 1.0 & 1.0 & 0.28 & 0.07 \\  & 0.1 & 0.0 & 0.0 & 0.28 & 0.06 \\ \hline \hline \end{tabular} \({}^{\star}\)–Statistically significant (\(p\)-value \(<\) 0.05) under a pairwise comparison when compared with the set within the group.  
\end{table}
Table 7: Cascade average strength (CAS) comparisons for deep cascades (best values in bold).  
Therefore, the ideal weight set should give less attention to retweets and importance to replies, and quotes should represent the interaction with higher priority. Among the remaining sets, \(2,8,9\) and \(10\), the maximum CAS was achieved by set 10 (44.7%). This set is also characterized by a smaller number of levels (2.38 levels on average), and a high percentage of edges passing thorough the \(root_{author}\) (61%), similar to the guideline set 0.0. Indeed, set 11 shows similarities to the guideline set 0.0 in terms of GCS, RFR and number of edges, but with a statistically significant difference in terms of CAS distribution, which is 2 p.p. (percentage points) lower than set 0.0 but respects the assumption of retweet bias.