Traditional socio-legal and legal scholarship have criticized the social structure of international arbitration. Some scholars have characterized this group of experts as a network of 'grand old men' and international arbitration as a 'white, male club.' However, faced with difficulties of data availability, they have failed to inform criticism with even basic social structure analysis. With unprecedented access to the historical data of arbitrator appointment in all arbitration proceedings under ICSID between 1972 and 2011, this article is the first to study the social structure of investor-State arbitrators. Using network analytics, a long-standing but recently popularized methodology for understanding social structures, the article shows the structure of connections between international arbitrators generated by formal appointments. Moreover, the visualizations in this article and the subsequent analytics provide insight into the arbitration world, gender imbalances, hierarchy, and evolution and generating dynamics. The article shows how the informal prestige and influence of jurists is far from equal, reveals the 'grand old men' (and women) or 'power-brokers' and 'bridges' in investor-State arbitration, and argues that arbitrators’ social capital may be generated through a process of preferential attachment. Arbitrators who have been appointed more frequently are more likely to attract further appointments.