This paper uses the methods of social network analysis to discover the structural patterns of cooperation that arose in response to a global traditional security problem. It does this by mapping compulsory and institutional power relations (Barnett and Duvall 2005) among actors responding to the proliferation of nuclear weapons since the end of the Cold War. For the institutional power measure, I use treaty and international agreement membership; and for the compulsory power measure, I use contractual obligations for nuclear expertise, materials, and technology. By mapping the relationships at the system level of world politics, including individual states as well as intergovernmental organizations (IGOs), transnational nongovernmental organizations (NGOs), and transnational corporations (TNCs), this paper finds a third relation among these actors, namely, structural power. It also demonstrates how a network approach to the constitution of system level world politics can produce knowledge not available to traditional methods.