Social network analysis (SNA) has much to offer sociology. However, there is little consideration of SNA in contemporary sociological theory (CST) although SNA developed in parallel with the consolidation of CST in the 1960s and 1970s. SNA championed its distinctiveness as 'structural analysis'. Nearly all current CST presents 'structure versus agency' as the crucial binary to differentiate mainstream theory, positivistic ontology and quantitative methodologies, on the one hand, from interactionist theories, qualitative methodologies and constructivist ontologies on the other. I argue that using structure as a simple binary means that the CST's notions of structure have become highly ambiguous and ill defined. Thus, for CST, 'structural analysis' has no purchase to describe the distinctiveness of SNA. I draw attention to the recent work of Lopez and Lopez and Scott that reclaims varied concepts of structure from previous literatures, including a concept of 'relational structure' that embraces SNA. The paper concludes that the work of Lopez is an important example of the 'visual' method of social theory practice advocated by Woodiwiss. Once we work with 'social-theoretical picturing' of structure, there is real potential to connect CST to the resources available in the visual, statistical and mathematical modeling developed by SNA.