  The large-scale structural ingredients of the brain and neural connectomes
have been identified in recent years. These are, similar to the features found
in many other real networks: the arrangement of brain regions into modules and
the presence of highly connected regions (hubs) forming rich-clubs. Here, we
examine how modules and hubs shape the collective dynamics on networks and we
find that both ingredients lead to the emergence of complex dynamics. Comparing
the connectomes of C. elegans, cats, macaques and humans to surrogate networks
in which either modules or hubs are destroyed, we find that functional
complexity always decreases in the perturbed networks. A comparison between
simulated and empirically obtained resting-state functional connectivity
indicates that the human brain, at rest, lies in a dynamical state that
reflects the largest complexity its anatomical connectome can host. Last, we
generalise the topology of neural connectomes into a new hierarchical network
model that successfully combines modular organisation with rich-club forming
hubs. This is achieved by centralising the cross-modular connections through a
preferential attachment rule. Our network model hosts more complex dynamics
than other hierarchical models widely used as benchmarks.
