The emergence of Big Data is both promising and challenging for social research. This article suggests that realising this promise has been restricted by the methods applied in social science research, which undermine our potential to apprehend the qualities that make Big Data so appealing, not least in relation to the sociology of networks and flows. With specific reference to the micro-blogging website Twitter, the article outlines a set of methodological principles for approaching these data that stand in contrast to previous research; and introduces a new tool for harvesting and analysing Twitter built on these principles. We work our argument through an analysis of Twitter data linked to political protest over UK university fees. Our approach transcends earlier methodological limitations to offer original insights into the flow of information and the actors and networks that emerge in this flow.