# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 1 Introduction
### Research Objective and Contributions  
Following the limitations of the existing approach to generate retweet cascade graphs, in this paper we introduce the concept of _interaction strength_ (IS), a novel metric that describes the strength of the link between two accounts in terms of reciprocal interactions, including quotes, replies, and retweets. The concept of the IS metric follows preceding work that highlighted the importance of relationship strength [8] for several tasks, including event and friend recommendation [9; 10]. However, to the best of our knowledge, this is the first time that user interaction strength has been studied to derive retweet cascade graphs.  
Based on this new metric, we propose two novel approaches to estimate retweet cascade graphs. The first approach is the interaction strength-based network (ISN), where the graph is constructed by maximizing the overall IS value computed for each pair of accounts. The friend list was used only for accounts that did not interact with other users, and for which it was not possible to find the IS values. The second approach is called interaction strength-based network with author's followers evaluation (ISN-AF). This approach is similar to ISN, but the author's follower list is exploited to generate the first level of the retweet cascade graph. Indeed, on Twitter a follower of the author of the original tweet (i.e., the root of the graph) can only retweet from the author himself/herself. It should be highlighted that both ISN and ISN-AF require to fetch the friends list for a limited number of accounts, whereas in the traditional approach it is necessary to fetch the friends list for each retweeters in the graph.  
Models aimed at constructing the retweet cascade graph suffer from the absence of a ground truth to check the correctness of the method. Despite this limitation, retweet information graphs can be extremely useful for analytics related to community detection and influencer node behavior. Following [11], we evaluated the proposed approaches in terms of network graph strength, considering several metrics.  
The novelty and contributions of this paper can be summarized as follows:  
* We introduce the concept of interaction strength (IS), a metric that indicates the strength of the link between two users;
* We propose two novel approaches based on IS to generate retweet cascade graphs--ISN and ISN-AF;
* ISN aims to maximize IS values for each pair of nodes in the graph;
* ISN-AF is similar to ISN, but the first level in the retweet cascade graph is based on the list of followers of the root user;
* Both of the proposed approaches are mainly based on information contained in the users' timelines, which can be conveniently retrieved through the free Twitter API service (compared to fetching the list of friends for each node as in the traditional approach, which is a substantially more time-consuming task);
* The source code is freely available on GitHub ([[https://github.com/paolazola/Interaction-strength-analysis-to-model-retweet-cascade-graphs](https://github.com/paolazola/Interaction-strength-analysis-to-model-retweet-cascade-graphs)]([https://github.com/paolazola/Interaction-strength-analysis-to-model-retweet-cascade-graphs](https://github.com/paolazola/Interaction-strength-analysis-to-model-retweet-cascade-graphs))).  
In Section 2 we provide a detailed overview on previous work about information propagation and retweet cascade prediction. Then, in Section 3 the proposed IS concept is described jointly with the ISN model; in Section 4 we report the description of the ISN-AF approach. Section 6 details the dataset, and Section 7 reports the analysis of the results related to the IS metrics; and the comparison among the proposed ISN and ISN-AF with respect to the baseline are in Section 8. Finally, Section 9 concludes the paper.