We present discussion graphs, a hyper-graph-based representation of social media discussions that captures both the structural features of the relationships among entities as well as the context of the discussions from which they were derived. Building on previous analyses of social media networks that focus on the strength of relationships between entities, our discussion graphs explicitly include contextual features such as who is participating in the discussions, when and where the discussions are occurring, and what else is being discussed in conjunction. There are two contributions of this work. First, we extend standard hyper-graph representations of networks to include the distribution of contexts surrounding discussions in social me...