  We study the emergence of coherence in complex networks of mutually coupled
non-identical elements. We uncover the precise dependence of the dynamical
coherence on the network connectivity, on the isolated dynamics of the elements
and the coupling function. These findings predict that in random graphs, the
enhancement of coherence is proportional to the mean degree. In locally
connected networks, coherence is no longer controlled by the mean degree, but
rather on how the mean degree scales with the network size. In these networks,
even when the coherence is absent, adding a fraction s of random connections
leads to an enhancement of coherence proportional to s. Our results provide a
way to control the emergent properties by the manipulation of the dynamics of
the elements and the network connectivity.
