  Delayed interactions are a common property of coupled natural systems and
therefore arise in a variety of different applications. For instance, signals
in neural or laser networks propagate at finite speed giving rise to delayed
connections. Such systems are often modeled by delay differential equations
with discrete delays. In realistic situations, these delays are not identical
on different connections. We show that by a componentwise timeshift
transformation it is often possible to reduce the number of different delays
and simplify the models without loss of information. We identify dynamic
invariants of this transformation, determine its capabilities to reduce the
number of delays and interpret these findings in terms of the topology of the
underlying graph. In particular, we show that networks with identical sums of
delay times along the fundamental semicycles are dynamically equivalent and we
provide a normal form for these systems. We illustrate the theory using a
network motif of coupled Mackey-Glass systems with 8 different time delays,
which can be reduced to an equivalent motif with three delays.
