  We consider networks of coupled maps where the connections between units
involve time delays. We show that, similar to the undelayed case, the
synchronization of the network depends on the connection topology,
characterized by the spectrum of the graph Laplacian. Consequently, scale-free
and random networks are capable of synchronizing despite the delayed flow of
information, whereas regular networks with nearest-neighbor connections and
their small-world variants generally exhibit poor synchronization. On the other
hand, connection delays can actually be conducive to synchronization, so that
it is possible for the delayed system to synchronize where the undelayed system
does not. Furthermore, the delays determine the synchronized dynamics, leading
to the emergence of a wide range of new collective behavior which the
individual units are incapable of producing in isolation.
