  In this article we study networks of coupled dynamical systems with
time-delayed connections. If two such networks hold different delays on the
connections it is in general possible that they exhibit different dynamical
behavior as well. We prove that for particular sets of delays this is not the
case. To this aim we introduce a componentwise timeshift transformation (CTT)
which allows to classify systems which possess equivalent dynamics, though
possibly different sets of connection delays. In particular, we show for a
large class of semiflows (including the case of delay differential equations)
that the stability of attractors is invariant under this transformation.
Moreover we show that each equivalence class which is mediated by the CTT
possesses a representative system in which the number of different delays is
not larger than the cycle space dimension of the underlying graph. We conclude
that the 'true' dimension of the corresponding parameter space of delays is in
general smaller than it appears at first glance.
