This article examines the population dynamics and viability of network weavers, which are organizations that provide network relations for others. An analysis of the population dynamics of the intergovernmental organizations (IGOs) that are the basis of the interstate networks that influenced global economic relations, peace, and democracy in the 1815–2000 period show that IGO founding and failure depends on the ease and value of specific interstate relations. Results indicate that network-weaving organizations are easier to operate when they encompass proximate and similar actors, yet they also reap rewards for bringing together otherwise disconnected actors, in particular actors with conflicts. Combined, these organizational processes can account for the high clustering and short-path distance between nodes that are characteristic of the endemic small-world network structure. Furthermore, the study shows that the concepts of legitimacy and competition can be applied to identify particular spaces in the network of bilateral relations that are more or less hospitable for IGOs.