Abstract: The anarchic international system is actually heavily structured: communities of states join together for common benefit; strong states form hierarchical relationships to enforce order and obtain preferred outcomes from weak states. We break from prior research to consider community and hierarchy together, as joint properties of an underlying network of states’ interactions, and argue for conditional effects of both community and hierarchy. Joint membership in a network community could reduce conflict between members of the community, if driven by the ability of strong states in more hierarchical communities to enforce order, but this may not be true in the absence of hierarchy. Hierarchical communities may engage in more, not less, conflict with each other. Using a time-dependent multilayer network model and specialized centrality measures, we find empirical support for these claims on two different networks, arms trade and commercial trade, and in so doing introduce a new measure of hierarchy.