On the Retweet Decay of the Evolutionary Retweet Graph.

Topological and structural properties of social networks, like Twitter, is of a major importance in order to understand the nature of user activities, for example how information propagates or how to identify influencing accounts. A deeper analysis of these properties may have a crucial impact on the design of new applications and of existing ones. In a social network there are different relations among nodes that can be defined and analyzed by keeping track of how the generated links evolve over time. So far, all evolutionary studies analyze the graph in a cumulative way, that is, once a link is inserted in a graph it is never eliminated [9,12]. However, in social networks like Twitter interactions are more volatile, and after a period of life they should die. In this paper, we consider the Retweet Graph, where links are generated by the retweet action made by an user. The life of a tweet is limited in time, and it spans from the time it is generated, to the last time it is retweeted. To take into account the dynamics of Twitter users, we consider a model in which, when a tweet expires, we delete all the edges representing the retweet action relative to this tweet and all users corresponding to involved nodes become inactive, unless they are alive with respect to a different retweeting activity. In particular, we define a new version of the usual Retweet Graph, the Dynamic Retweet Graph (DRG): when a tweet has been retweeted for the last time all the edges related to this tweet are deleted. This allows to model the decay of tweet relavance in Twitter. To evaluate the structural properties of a DRG, we consider three different Twitter streams, derived by monitoring the Twitter flow on three different contexts: two of them are based on a specific event (the 2015 Black Friday and the 2015 World Series) while the third is the Firehose of the whole Twitter stream, filtered by the Italian language. We study the differences between the DRG graphs and the corresponding cumulative ones by comparing standard metrics for social networks, such as average distance, clustering coefficient, in-degree and out-degree distributions. The analysis shows an important difference between the cumulative graphs and the corresponding DRGs, both on the way they grow, and on the way the observed measures evolve.