Moving beyond the Twitter follow graph

The study of the topological properties of graphs derived from social network platforms has a great importance both from the social and from the information point of view; furthermore, it has a big impact on designing new applications and in improving already existing services. Surprisingly, the research community seems to have mainly focused its efforts just on studying the most intuitive and explicit graphs, such as the follower graph of the Twitter platform, or the Facebook friends' graph: consequently, a lot of valuable information is still hidden and it is waiting to be explored and exploited. In this paper we introduce a new type of graph modeling behavior of Twitter users: the mention graph. Then we show how to easily build instances of this graphs starting from the Twitter stream, and we report the results of an experimentation aimed to compare the proposed graph with other graphs already analyzed in the literature, by using some standard social network analysis metrics.