# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 9 Conclusions  
In this paper we have proposed two novel approaches to derive retweet cascade graphs, both based on the concept of interaction strength (IS). The obtained information graphs can be useful for further analysis like the detection of influencer nodes and communities. Differently from state-of-the-art approaches that are mainly based on users' social networks, the IS metric aims to enable a realistic estimation of Twitter information propagation considering the trust relationships among users, and giving more importance to frequent and strong interactions instead of considering the simple following relation. The two proposed approaches are the interaction strength-based network (ISN) and the interaction strength-based network with author's followers evaluation (ISN-AF). The ISN approach consists of two steps: the first phase aims to discover interactions among nodes involved in the retweet cascade, identifying links able to maximize the cascade average strength (CAS); then, for the remaining nodes the state-of-the-art approach based on nodes' social network is adopted. The ISN-AF approach also has a preliminary analysis of \(root_{author}\) followers, which are used to generate the first level fo the cascade graph. This leads to an even more realistic graph, but also has some limitations.  
The analysis and, in particular, the comparison with the baseline method show the differences between the proposed approaches, and their ability to highlight node importance in the retweet information propagation path. Notably, ISN and ISN-AF are able to reduce the impact of sparse nodes, diminishing the isolated connected components, and thus giving a more complete view of the retweet propagation phenomena. Hence, the study of the different propagation paths derived by ISN and ISN-AF (Figure 10) can offer a starting point for different future application such as social bot detection, inauthentic coordinated behaviors, etc. [36]. Moreover, differently from existing literature models, the proposed ISN and ISN-AF cascades can be evaluated through the CAS value, which gives to the analyst a proxy of the goodness of the obtained graph.  
Notwithstanding the high number of experiments conducted, the absence of a ground truth is a limitation of the proposed evaluation. Additionally, further analysis may be performed in order to optimize the interaction weights starting from the findings achieved in this paper. Other aspects that we intend to explore in future work are the tweet contents and the sentiments included in quotes and replies. Moreover, given the obtained weighted retweet cascade graph, an interesting future application may consider community detection and reinforce the derived cascades based on modularity measure.  
In conclusion, we believe that the proposed approaches represent a promising alternative solution to the problem of Twitter retweet cascade graph constructions, as they highlight nodes' importance in information flows and overcome some of the limitations of the models based only on social network information.  
Conceptualization, P.Z., G.C.; methodology, P.Z.; software, P.Z.; validation, P.Z., G.C. and M.M.; formal analysis, P.Z.; investigation, P.Z.; resources, P.Z.; data curation, P.Z.; writing-original draft preparation, P.Z.; writing-review and editing, P.Z., G.C., M.M.; visualization, P.Z.; supervision, M.T.; project administration, M.T.; funding acquisition, M.T. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported by the scheme 'INFRAIA-01-2018-2019: Research and Innovation action', Grant Agreement n. 871042 'SoBigData++: European Integrated Infrastructure for Social Mining and Big Data Analytics.  
We want to thank the anonymous reviewers for their useful comments and suggestions.  
The authors declare no conflict of interest.