# Interaction Strength Analysis to Model Retweet Cascade Graphs
## 1 Introduction  
In recent years, the explosion of Web 2.0, blogs, microblogs and online social media dramatically changed information consumption and spreading. A recent survey revealed that, for the first time in the history, United States people consume more news from social media than newspapers ([[https://www.cnbc.com/2018/12/10/social-media-more-popular-than-newspapers-for-news-pew.html](https://www.cnbc.com/2018/12/10/social-media-more-popular-than-newspapers-for-news-pew.html)]([https://www.cnbc.com/2018/12/10/social-media-more-popular-than-newspapers-for-news-pew.html](https://www.cnbc.com/2018/12/10/social-media-more-popular-than-newspapers-for-news-pew.html))). Thus, tracking the information diffusion, especially in online communities, is a very important step which is useful for many applications, such as early warning systems, social bot and community detection, user location prediction, financial recommendations, marketing campaign effectiveness, political mobilization and protests, etc. [1; 2; 3; 4].  
Among online communities, social media represent preferable channels for information diffusion, and with more than 330 million monthly active users, Twitter is one of the most used social media platforms which is often considered as an information network [5; 6]. Twitter offers four possible actions to express interest in specific content: favorite, reply, quote and retweet. Replying or liking a tweet does not involve the spread of the content, whereas quotes and retweets are actions used to share information with a wider audience. However, quoting or retweeting a message may indicate a different user behavior. A retweet is often considered an endorsement, i.e., the user supports the original tweet's content, whereas quoting may be done in order to express a different idea [7].  
In order to understand the connections among users, it is important to consider not only their social networks but also the way they interact with information, especially through retweets [5; 6]. Thanks to the Twitter API service, it is possible to collect a huge amount of information regarding tweets, accounts, users timelines and social networks (i.e., following and followers). However,the Twitter API does not provide complete information about retweets and their propagation paths. More precisely, the only information carried by a retweet is the original author of the tweet, whereas possible intermediate steps (i.e., retweeting from a retweeter) are lost.  
To estimate retweet cascade graphs, previous studies typically adopted strategies based on social network information (i.e., friends and followers) in conjunction with temporal information. These studies exploited the fact that users tend to interact more often with newer tweets [7], and thus a user is more likely to retweet the last friend who retweeted content. However, this approach is no longer a reliable way of estimating retweet graphs, as Twitter does not show content based on simple reverse chronological order, but according to user interests, trending topics and interactions ([[https://blog.hootsuite.com/twitter-algorithm/](https://blog.hootsuite.com/twitter-algorithm/)]([https://blog.hootsuite.com/twitter-algorithm/](https://blog.hootsuite.com/twitter-algorithm/))).  
Another factor that needs to be considered is the time required to fetch all the required social network information. Due to the Twitter API rate limits, the time required to collect the list of friends and followers is six times greater with respect to downloading the user's timeline ([[https://developer.twitter.com/en/docs/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids](https://developer.twitter.com/en/docs/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids)]([https://developer.twitter.com/en/docs/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids](https://developer.twitter.com/en/docs/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids))), on average.