  Which topics spark the most heated debates on social media? Identifying those
topics is not only interesting from a societal point of view, but also allows
the filtering and aggregation of social media content for disseminating news
stories. In this paper, we perform a systematic methodological study of
controversy detection by using the content and the network structure of social
media.
  Unlike previous work, rather than study controversy in a single hand-picked
topic and use domain specific knowledge, we take a general approach to study
topics in any domain. Our approach to quantifying controversy is based on a
graph-based three-stage pipeline, which involves (i) building a conversation
graph about a topic; (ii) partitioning the conversation graph to identify
potential sides of the controversy; and (iii) measuring the amount of
controversy from characteristics of the graph.
  We perform an extensive comparison of controversy measures, different
graph-building approaches, and data sources. We use both controversial and
non-controversial topics on Twitter, as well as other external datasets. We
find that our new random-walk-based measure outperforms existing ones in
capturing the intuitive notion of controversy, and show that content features
are vastly less helpful in this task.
