# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 7 Evaluation of IS Weights
### Experimental Results on the Entire Cascade Sample  
Starting from the guideline sets' results in Table 5, we got that the set 0.0, which describes the proposed model when all the interactions have the same weight, reaches an average CAS of 87% with 91% of edges passing from the \(root_{author}\) (RFR) and less than the 2% of SNI. A growing SNI is visible for the guideline sets 0.1, 0.3 and 0.2, especially for the last two which are characterized by an average CAS of 84%. Guideline set 0.1 is, in general, preferable to sets 0.2 and 0.3 in terms of CAS. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Full Dataset** & **Sampled Dataset** \\ \hline Tweets Count & 506,147 & 16,304 \\ Unique Users Count & 102,468 & 41,592 \\ Retweets Count & 683,189 & 112,188 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dataset description. Figure 3: Correlation matrix among the cascades’ evaluation metrics. Concerning the analysis of the full sample of cascades computed, Table 6 reports the average metrics for each set of weights in the experimental setups. In general, all the proposed experiments reached a valuable CAS which was between 83% and 87%. The lowest CAS values (around 83%) were achieved by sets 1, 2 and 8, which were also characterized by a smaller retweet weight (0.0 and 0.1 respectively). In general, the proposed approach limits the incidence of sparse nodes (SNI), which is around 2%, with an average cascade depth below 1. However, these results are computed on the entire sample of \(16,304\) tweets, thereby including cascades with few retweets that are characterized by a CAS value of one. Figures 4 and 5 plot on the x-axis the cascade depth, while on the y-axis there is the CAS achieved by each cascade for the guideline and experimental sets, respectively. Figures 4 and 5 show the strong negative correlation between CAS and depth. The negative correlation is common among all the weights sets (both for guideline and experimental set), but it shows different behavior according to the incidence of retweets, quotes and replies. For instance, cascades with a higher retweet impact show a more linear decay without drops (sets \(\{0.0,5\}\)), but a more interesting piece evidence is about quotes and replies effects. In fact, sets with identical retweet weight but with quote importance smaller than replies exhibit more variable dynamics with drops for deeper cascades (e.g., set 0.2 versus set 0.3 and set 3 versus set 4). \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Set** & **Edge Count** & **CCC** & **GCS (\%)** & **RFR (\%)** & **GRC (\%)** & **CAS (\%)** & **Depth** & **SNI (\%)** \\ \hline
1 & 5.88 & 1.08 & 6.27 & 93.61 & 6.12 & 83.53 \({}^{*,\circ,\bullet}\) & 0.53 & 2.04 \\
2 & 5.89 & 1.08 & 6.25 & 93.59 & 6.12 & 82.93 \({}^{*,\circ,\bullet}\) & 0.53 & 2.01 \\
3 & 5.89 & 1.08 & 6.29 & 93.77 & 6.17 & 86.32 \({}^{\dagger,\bullet}\) & 0.53 & 2.08 \\
4 & 5.89 & 1.08 & 6.25 & 93.81 & 6.19 & 87.23 \({}^{\circ,\bullet}\) & 0.52 & 1.98 \\
5 & 5.80 & 1.08 & 6.20 & 93.77 & 6.06 & 84.63 \({}^{*,\circ}\) & 0.52 & 2.03 \\
6 & 5.80 & 1.08 & 6.20 & 93.74 & 6.06 & 84.21 \({}^{\dagger,\circ}\) & 0.52 & 2.04 \\
7 & 5.80 & 1.08 & 6.22 & 93.78 & 6.07 & 84.80 \({}^{\dagger,\circ,\bullet}\) & 0.52 & 2.11 \\
8 & 5.88 & 1.08 & 6.28 & 93.62 & 6.15 & 83.45 \({}^{*,\circ,\bullet}\) & 0.53 & 1.98 \\
9 & 5.88 & 1.08 & 6.29 & 95.73269 & 5.76 & 83.67 \({}^{\dagger,\circ,\bullet}\) & 0.54 & 1.98 \\
10 & 5.88 & 1.08 & 6.31 & 93.79 & 6.18 & 86.63 \({}^{\dagger,\circ,\bullet}\) & 0.53 & 2.00 \\ \hline \hline \end{tabular} \({}^{*,\dagger,\circ,\bullet}\)  
\end{table} 
Table 6: Average metrics for each weight set in the experimental setups, computed on the whole dataset.