  Although it is unambiguously agreed that structure plays a fundamental role
in shaping the dynamics of complex systems, this intricate relationship still
remains unclear. We investigate a general computational transformation by which
we can map the network topology directly to the dynamical patterns emergent on
it -- independent of the nature of the dynamical process. We find that many
seemingly diverse dynamical processes such as coupled oscillators and diffusion
phenomena can all be understood and unified through this same procedure. Using
the multiscale complexity measure derived form the structure-dynamics
transformation, we find that the topological features like hierarchy,
heterogeneity and modularity all result in higher complexity. This result
suggests a universal principle: it is the desire for functional diversity that
drives the evolution of network architecture.
