# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 8 ISN, ISN-AF and Baseline Comparisons  
In this section we compute the retweet cascade graph for all the 16,304 tweets using the proposed ISN approach based on IS and, whenever the IS value is not available, on social network information. Moreover, we also report the results of the ISN-AF approach, where a preliminary check on \(root_{author}\) followers is performed to generate the first level of the cascade graph. Results are then compared with a baseline model proposed by [PERSON] et al. [11]. Table 9 reports the metrics for our two approaches and the baseline; the CAS value is only available for the IS and ISN-AF (the baseline model is not based on IS) achieving 85.29% and the 94.7% CAS, respectively. Hence, ISN-AF, which exploits the author's followers list, outperforms ISN in terms of CAS. This is due to the probability equal to one assigned to edges connecting nodes to the \(root_{author}\) \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Set** & **Edge Count** & **CCC** & **GCS (\%)** & **RFR (\%)** & **GRC (\%)** & **CAS (\%)** & **Depth** & **SNI (\%)** \\ \hline
0.0 & 46.17 & 1.54 & 41.96 & 60.76 & 32.84 & 46.77 \({}^{\circ,\bullet}\) & 2.37 & 16.33 \\
0.1 & 46.17 & 1.56 & 42.31 & 60.29 & 32.71 & 41.45 \({}^{\circ,\bullet}\) & 2.37 & 16.96 \\
0.2 & 46.21 & 1.56 & 42.09 & 59.78 & 32.54 & 38.34 \({}^{\circ,\bullet}\) & 2.40 & 17.56 \\
0.3 & 46.21 & 1.55 & 42.28 & 59.80 & 32.58 & 38.46 \({}^{\circ,\bullet}\) & 2.40 & 17.43 \\ ine 1 & 46.17 & 1.55 & 42.13 & 59.37 & 32.35 & 36.09 \({}^{\circ,\bullet,\bullet}\) & 2.43 & 16.81 \\
2 & 46.21 & 1.52 & 41.92 & 59.43 & 32.27 & 35.90 \({}^{\circ,\bullet,\bullet}\) & 2.43 & 16.54 \\
3 & 46.21 & 1.55 & 42.28 & 60.51 & 32.65 & 43.65 \({}^{\circ,\bullet}\) & 2.39 & 17.14 \\
4 & 46.21 & 1.52 & 41.95 & 60.70 & 32.82 & 48.31 \({}^{\circ}\) & 2.36 & 16.33 \\
5 & 46.15 & 1.56 & 42.16 & 59.75 & 32.56 & 38.80 \({}^{\circ,\bullet,\bullet}\) & 2.39 & 16.96 \\
6 & 46.15 & 1.56 & 42.09 & 59.58 & 32.54 & 37.71 \({}^{\circ,\bullet,\bullet}\) & 2.39 & 17.08 \\
7 & 46.15 & 1.56 & 42.31 & 59.83 & 32.58 & 39.34 \({}^{\circ,\bullet}\) & 2.39 & 17.64 \\
8 & 46.17 & 1.55 & 42.20 & 59.48 & 32.53 & 36.39 \({}^{\circ,\bullet}\) & 2.41 & 16.35 \\
9 & 46.17 & 1.55 & 42.12 & 55.36 & 31.12 & 45.43 \({}^{\circ,\bullet}\) & 2.37 & 16.43 \\
10 & 46.17 & 1.55 & 42.46 & 60.63 & 32.73 & 44.74 \({}^{\circ,\bullet,\bullet}\) & 2.38 & 16.47 \\ \hline \hline \end{tabular} \({}^{\star,\circ,\bullet}\)—Statistically significant (\(p\)-value \(<\) 0.05) under a pairwise comparison when compared with the guideline sets: 0.0 (\({}^{\circ}\)), 0.1 (\({}^{\dagger}\)), 0.2 (\({}^{\circ}\)), 0.3 (\({}^{\star}\)).  
\end{table} 
Table 8: Average metrics for all the setups (guideline and experimental), computed on the cascades with more than five nodes. Figure 6: CAS on the set of tweets with at least five retweets. whenever the node is in the author's followers list. Indeed, ISN-AF creates denser cascades around the root node, as indicate by the higher RFR and GRC values. However, as argued in Section 1, methods based on friends/followers lists have two major limitations: the computational time required to collect the information and, most importantly, the temporal gap between the date in which the retweet is collected and the date when the followers list is fetched. This latter limitation could introduce a form of bias in the cascade. Comparing the proposed methods with respect to the baseline, a significant difference is apparent regarding the SNI: the two proposed models have an incidence of sparse nodes below 2%, whereas the baseline has an average SNI above 6%. This lower SNI could be linked to the ability of the proposed approach to overcome the limitations of the baseline, as discussed in Sections 1 and 2. For instance, Twitter accounts might have a private network, which is not accessible, thus the baseline approach based has to classify these node as sparse, whereas the proposed approaches may still be able to find some interactions and find a link for these node in the graph.