A traditional view of power in politics is that it comes from the possession of important resources. The relative possession of resources is thought to provide actors such as people, organizations, and states with means of coercion or influence over others. This traditional view is highly limiting, since power also comes from ties (patterns of association) that link together actors in networks. These ties, whether material (like trade flows) or social (like friendship), determine an actor’s ability to have access to, make connections between, or quickly spread resources to, other actors. An actor’s relative position in a network formed by these ties thus provides another important source of influence over others. In this article, we introduce three classes of network centrality positions (degree, betweenness, and closeness), explain the advantages of each, and demonstrate that network notions of power that derive from centrality can significantly inform the study of politics.