Topological properties of graphs derived from social network platforms, like Twitter, give important insights on the nature of the social activities or on the way information spreads over the network. It may have also a relevant impact on designing new applications and improving already existing services. Different types of relations among the nodes define different graphs th at can be analyzed, by tracking how relations evolve over time. Usually, this is performed in a cumulative way: once an edge is inserted, it is never deleted, see Leskovec et al. (2005) and Leskovec et al. (2010) . However, the tweet life is limited, spanning from its birth to the very last retweet it receives. Therefore, we want to analyze the dynamics of evolutionary graphs, that is deleting tweets and thus edges among the nodes when they naturally expire as well as accounts that become therefore inactive. We introduce a variant of the retweet graph which takes into account the dynamics of Twitter users: Dynamic Retweet Graph (DRG) . In a DRG , once a tweet has been retweeted the last time all the edges representing this tweet are deleted, to model the decay of tweet life in the social platform. We analyze the characteristics of this graph using three different Twitter streams, built on three different contexts: two are event based (the 2015 Black Friday and the 2015 World Series), the third is the firehose of the whole Twitter stream, filtered by the Italian language. We use some standard social network analysis metrics to compare the structural properties of the DRG graph with cumulative evolving graphs.