  We suggest a new perspective of research towards understanding the relations
between structure and dynamics of a complex network: Can we design a network,
e.g. by modifying the features of units or interactions, such that it exhibits
a desired dynamics? Here we present a case study where we positively answer
this question analytically for networks of spiking neural oscillators. First,
we present a method of finding the set of all networks (defined by all mutual
coupling strengths) that exhibit an arbitrary given periodic pattern of spikes
as an invariant solution. In such a pattern all the spike times of all the
neurons are exactly predefined. The method is very general as it covers
networks of different types of neurons, excitatory and inhibitory couplings,
interaction delays that may be heterogeneously distributed, and arbitrary
network connectivities. Second, we show how to design networks if further
restrictions are imposed, for instance by predefining the detailed network
connectivity. We illustrate the applicability of the method by examples of
Erd\"{o}s-R\'{e}nyi and power-law random networks. Third, the method can be
used to design networks that optimize network properties. To illustrate this
idea, we design networks that exhibit a predefined pattern dynamics while at
the same time minimizing the networks' wiring costs.
