Much research on higher education has engaged with the concept of "world-class" universities and the complementary surge of interest in global university rankings. Literature takes a variety of positions on these intertwined phenomena, from vocal support of rankings and "world-class" aspirations to critical analyses of their influence and ideological underpinnings. Despite these differences, there is widespread consensus on the obsession with "world-class" status and the emergence of a new global field of competition (Altbach 2004; King, 2010; Robertson 2012; Tapper and Filippakoub, 2009). This field is disembedded from-but not entirely independent of-national systems of higher education and organized through rankings that create positional competition around research output and reputation (Marginson and van der Wende, 2007). This paper seeks to understand how universities in global rankings relate to one another through social media as a way to better understand reputation and prestige in the field of "world-class" universities. Specifically, it examines the extent to which rankings are reflected in the structure of social media networks and whether those that occupy the top spaces in global rankings tend to associate with one another as a way of reproducing status. While social media networks are less academically focused than those of research collaboration (Moody, 2004) and less formal than institutional consortia (e.g. the World University Network and Universitas 21), they are highly visible, widely accessible and therefore a good measure of how institutions position themselves to maximise prestige within a globally competitive field. Social media are also an increasingly popular and influential means for public engagement and an important component of institutional branding. The paper uses social network analysis and network modelling to examine universities' interactions on Twitter to study how relationships of prestige and positional competition operate in social media networks. Networks are conceptualised and operationalized at the institutional level, with a focus on how networks relate to institutions' reputation and prestige. It begins by discussing literature on "world-class" universities, global university rankings, and network perspectives on global higher education, and then introduces social network analysis, network modelling and sources of data. The analysis presents descriptive network statistics, data visualisations, and results of network models, and the paper concludes by discussing their significance for research on global higher education. Literature Review: "World-Class" and "Network" Universities Recent years have witnessed an obsession with "world-class" universities and global rankings, which can be traced to a steady growth in "world class" terminology since the turn of the century (Ramirez and Tiplic, 2014). Since then, creating "world-class" universities has become an obsession to the extent that "no country feels it can do without one" (Altbach, 2004). The emergence of "world-clas...