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International relations research has regarded networks as a particular mode of organization, distinguished from markets or state hierarchies. In contrast, network analysis permits the investigation and measurement of network structures—emergent properties of persistent patterns of relations among agents that can define, enable, and constrain those agents. Network analysis offers both a toolkit for identifying and measuring the structural properties of networks and a set of theories, typically drawn from contexts outside international relations, that relate structures to outcomes. Network analysis challenges conventional views of power in international relations by defining network power in three different ways: access, brokerage, and exit options. Two issues are particularly important to international relations: the ability of actors to increase their power by enhancing and exploiting their network positions, and the fungibility of network power. The value of network analysis in international relations has been demonstrated in precise description of international networks, investigation of network effects on key international outcomes, testing of existing network theory in the context of international relations, and development of new sources of data. Partial or faulty incorporation of network analysis, however, risks trivial conclusions, unproven assertions, and measures without meaning. A three-part agenda is proposed for future application of network analysis to international relations: import the toolkit to deepen research on international networks; test existing network theories in the domain of international relations; and test international relations theories using the tools of network analysis.