  We study the interplay between network topology and complex space-time
patterns and introduce a concept to analytically predict complex patterns in
networks of Stuart-Landau oscillators with linear symmetric and instantaneous
coupling based solely on the network topology. These patterns consist of
partial amplitude death and partial synchronization and are found to exist in
large variety for all undirected networks of up to 5 nodes. The underlying
concept is proved to be robust with respect to frequency mismatch and can also
be extended to larger networks. In addition it directly links the stability of
complete in-phase synchronization to only a small subset of topological
eigenvalues of a network.
