  Complex dynamical networks appear in a wide range of physical, biological,
and engineering systems. The coupling of subsystems with varying time scales
often results in multirate behavior. During the simulation of highly integrated
circuits, for example, only a few elements underlie changing signals whereas
the major part -- usually up to 80 or even 90 per cent -- remains latent.
Standard integration schemes discretize the entire circuit with a single step
size which is mainly limited by the accuracy requirements of the rapidly
changing subcircuits. It is of a particular interest to speed up the simulation
without a significant loss of accuracy. By exploiting the latency of the
system, only a fraction of the equations has to be formulated and solved at a
given time point.
  G\"unther and Rentrop suggest that multirate strategies must be based both on
the numerical information of the integration scheme and on the topology of the
circuit. In this paper, we will introduce a directed graph describing the
interdependency of the underlying system and propose Runge--Kutta methods which
utilize the signal flow of the system in order to identify and exploit inactive
regions. Furthermore, we describe an extension of these methods to identify and
exploit periodic subsystems.
