Social network analysis (SNA) has emerged as a powerful and practical method for representing and analysing social phenomena, due at least partly to the increasing availability of ‘big data’ and socially-generated digital trace data. Yet why does SNA remain a somewhat niche area for contemporary sociology, even though it was arguably born out of the field? Certainly there are technical and methodological barriers that one might explore via dualisms such as quantitative/qualitative, positivist/interpretivist, and so forth. In this seminar, I explore another idea: that the way SNA has been mathematically formalised may actually serve to subjugate social phenomena into a system of representation that obscures the complex and contextual social realities that we wish to describe/map and understand. As a point of departure I draw upon Foucault’s discussion of the 16th century painting Las Meninas (by Diego Vel?zquez) to explore how visual representations (paintings, diagrams, networks) do not simply reflect objective realities, but are sites of uncertainty between reality and representation. Drawing loosely on Foucault’s argument and using illustrative examples from my own research, I examine and problematise networks in terms of how these objects represent and construct social realities. I argue that graph theory, which is the standardised mathematical formalism underpinning SNA, is a sort of ‘double-edged sword’ for sociology. On the one hand, it is highly useful for rendering the social computable, particularly in the era of big data. On the other hand, I argue that graph theory represents entities and relations in a way that is surprisingly problematic—indeed, it is logically incompatible with contemporary social theories such as Actor-Network Theory. Following this, I report on preliminary research that attempts to address these problems by using the mathematics of hypergraphs and a kind of reflexive approach to network representation and descriptive analysis. The discussion is augmented through the demonstration of various tools, diagrams, and findings from my current research projects and interests. I conclude with a brief reflection on how this research might provide theoretical and methodological pathways to bridging the gap between contemporary sociology and the powerful methods and computational tools of SNA.