The construction of social network graphs from online networks data has become nowadays a common track to analyze these data. Typical research questions in this domain are related to profile building, interest’s recommendation, and trending topics prediction. However, few work has been devoted to the analysis of the evolution of very short and unpredictable events, called polemics. Also, experts do not use tools coming from social network graphs analysis and classical graph theory for this analysis. In this way, this article shows that such analysis lead to a colossal amount of data collected from public social sources like Twitter. The main problem is collecting enough evidences about a non-predictable event, which requires capturing a complete history before and during the course of this event, and processing them. To cope with this problem, while waiting for an event, we captured social data without filtering it, which required more than a TB of disk space. Then, we conduct a time-related social network analysis. The first one is dedicated to the study of the evolution of the actor interactions, using time-series built from a total of 33 graph theory metrics. A Big Data pipeline allows us to validate these techniques on a complex dataset of 284 millions of tweets, analyzing 56 days of the Volkswagen scandal.