With the rise of social media as an important channel for the debate and
discussion of public affairs, online social networks such as Twitter have
become important platforms for public information and engagement by policy
makers. To communicate effectively through Twitter, policy makers need to
understand how influence and interest propagate within its network of users. In
this chapter we use graph-theoretic methods to analyse the Twitter debate
surrounding NHS England's controversial care.data scheme. Directionality is a
crucial feature of the Twitter social graph - information flows from the
followed to the followers - but is often ignored in social network analyses;
our methods are based on the behaviour of dynamic processes on the network and
can be applied naturally to directed networks. We uncover robust communities of
users and show that these communities reflect how information flows through the
Twitter network. We are also able to classify users by their differing roles in
directing the flow of information through the network. Our methods and results
will be useful to policy makers who would like to use Twitter effectively as a
communication medium.