This article (26 page PDF) analyzes patterns of social media connectivity as a means of detecting and quantifying controversy in Twitter discussions. The main work is undertaken by algorithms that partition the conversation graph to identify potential sides of the controversy, specifically, "a state-of-the-art off-the-shelf algorithm, METIS." The quantification is probably the most problematic aspect of this. We could perhaps look at the graph and simply select the more controversial debates just by the shape, but to quantify requires an actual measurement. Here's what they do: "The measure captures the intuition of how likely a random user on either side is to be exposed to authoritative content from the opposing side." Summaries from MIT Technical Review and Olga Ioannou.
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