In this paper, we analyze the complexity of functional programs written in the interaction net computation model, an asynchronous, parallel and confluent model that generalize linear logic proof nets. Relying on the use of sized and scheduled types, we establish concrete time, space and space-time complexity bounds for both sequential and parallel reductions of interaction-net systems by suitably assigning complexity potentials to typed nodes. The relevance of this approach is illustrated on archetypal programming examples. The provided analysis is precise, compositional and is, in theory, not restricted to particular complexity classes.